Linear Algebra Examples

$x = - 3 - 2 i$ , $y = x \cdot (x + 2) \cdot (x + 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1

Simplify.

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Step 1.1

Apply the distributive property.

$x = - 3 - 2 i, y = (x \cdot x + x \cdot 2) \cdot (x + 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = (x^{2} + x \cdot 2) \cdot (x + 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.3

Move $2$ to the left of $x$ .

$x = - 3 - 2 i, y = (x^{2} + 2 \cdot x) \cdot (x + 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.4

Expand $(x^{2} + 2 x) (x + 6)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$x = - 3 - 2 i, y = (x^{2} (x + 6) + 2 x (x + 6)) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.4.2

Apply the distributive property.

$x = - 3 - 2 i, y = (x^{2} x + x^{2} \cdot 6 + 2 x (x + 6)) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.4.3

Apply the distributive property.

$x = - 3 - 2 i, y = (x^{2} x + x^{2} \cdot 6 + 2 x \cdot x + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.5.1.1.1

Multiply $x^{2}$ by $x$ .

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Step 1.5.1.1.1.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{2} x^{1} + x^{2} \cdot 6 + 2 x \cdot x + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{2 + 1} + x^{2} \cdot 6 + 2 x \cdot x + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.1.2

Add $2$ and $1$ .

$x = - 3 - 2 i, y = (x^{3} + x^{2} \cdot 6 + 2 x \cdot x + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.2

Move $6$ to the left of $x^{2}$ .

$x = - 3 - 2 i, y = (x^{3} + 6 \cdot x^{2} + 2 x \cdot x + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.5.1.3.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{3} + 6 x^{2} + 2 (x \cdot x) + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.3.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = (x^{3} + 6 x^{2} + 2 x^{2} + 2 x \cdot 6) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.1.4

Multiply $6$ by $2$ .

$x = - 3 - 2 i, y = (x^{3} + 6 x^{2} + 2 x^{2} + 12 x) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.5.2

Add $6 x^{2}$ and $2 x^{2}$ .

$x = - 3 - 2 i, y = (x^{3} + 8 x^{2} + 12 x) \cdot (x + 3 - 2 i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.6

Expand $(x^{3} + 8 x^{2} + 12 x) (x + 3 - 2 i)$ by multiplying each term in the first expression by each term in the second expression.

$x = - 3 - 2 i, y = (x^{3} x + x^{3} \cdot 3 + x^{3} (- 2 i) + 8 x^{2} x + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.7.1.1

Multiply $x^{3}$ by $x$ .

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Step 1.7.1.1.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{3} x^{1} + x^{3} \cdot 3 + x^{3} (- 2 i) + 8 x^{2} x + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{3 + 1} + x^{3} \cdot 3 + x^{3} (- 2 i) + 8 x^{2} x + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.1.2

Add $3$ and $1$ .

$x = - 3 - 2 i, y = (x^{4} + x^{3} \cdot 3 + x^{3} (- 2 i) + 8 x^{2} x + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.2

Move $3$ to the left of $x^{3}$ .

$x = - 3 - 2 i, y = (x^{4} + 3 \cdot x^{3} + x^{3} (- 2 i) + 8 x^{2} x + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.7.3.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 (x \cdot x^{2}) + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.3.2

Multiply $x$ by $x^{2}$ .

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Step 1.7.3.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 (x^{1} x^{2}) + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{1 + 2} + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.3.3

Add $1$ and $2$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 8 x^{2} \cdot 3 + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.4

Multiply $3$ by $8$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} + 8 x^{2} (- 2 i) + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.5

Multiply $- 2$ by $8$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} - 16 x^{2} i + 12 x \cdot x + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.6

Multiply $x$ by $x$ by adding the exponents.

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Step 1.7.6.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} - 16 x^{2} i + 12 (x \cdot x) + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.6.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} - 16 x^{2} i + 12 x^{2} + 12 x \cdot 3 + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.7

Multiply $3$ by $12$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} - 16 x^{2} i + 12 x^{2} + 36 x + 12 x (- 2 i)) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.7.8

Multiply $- 2$ by $12$ .

$x = - 3 - 2 i, y = (x^{4} + 3 x^{3} + x^{3} (- 2 i) + 8 x^{3} + 24 x^{2} - 16 x^{2} i + 12 x^{2} + 36 x - 24 x i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.8

Add $3 x^{3}$ and $8 x^{3}$ .

$x = - 3 - 2 i, y = (x^{4} + 11 x^{3} + x^{3} (- 2 i) + 24 x^{2} - 16 x^{2} i + 12 x^{2} + 36 x - 24 x i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.9

Add $24 x^{2}$ and $12 x^{2}$ .

$x = - 3 - 2 i, y = (x^{4} + 11 x^{3} + x^{3} (- 2 i) + 36 x^{2} - 16 x^{2} i + 36 x - 24 x i) \cdot (x + 9 + 6 i) \cdot (x + 9 - 6 i)$

Step 1.10

Expand $(x^{4} + 11 x^{3} + x^{3} (- 2 i) + 36 x^{2} - 16 x^{2} i + 36 x - 24 x i) (x + 9 + 6 i)$ by multiplying each term in the first expression by each term in the second expression.

$x = - 3 - 2 i, y = (x^{4} x + x^{4} \cdot 9 + x^{4} (6 i) + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11

Simplify each term.

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Step 1.11.1

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 1.11.1.1

Multiply $x^{4}$ by $x$ .

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Step 1.11.1.1.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{4} x^{1} + x^{4} \cdot 9 + x^{4} (6 i) + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{4 + 1} + x^{4} \cdot 9 + x^{4} (6 i) + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.1.2

Add $4$ and $1$ .

$x = - 3 - 2 i, y = (x^{5} + x^{4} \cdot 9 + x^{4} (6 i) + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.2

Move $9$ to the left of $x^{4}$ .

$x = - 3 - 2 i, y = (x^{5} + 9 \cdot x^{4} + x^{4} (6 i) + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.3

Move $6$ to the left of $x^{4}$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 \cdot x^{4} i + 11 x^{3} x + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.4

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.11.4.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 (x \cdot x^{3}) + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.4.2

Multiply $x$ by $x^{3}$ .

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Step 1.11.4.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 (x^{1} x^{3}) + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{1 + 3} + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.4.3

Add $1$ and $3$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 11 x^{3} \cdot 9 + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.5

Multiply $9$ by $11$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 11 x^{3} (6 i) + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.6

Multiply $6$ by $11$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{3} (- 2 i) x + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.7

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.11.7.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x \cdot x^{3} (- 2 i) + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.7.2

Multiply $x$ by $x^{3}$ .

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Step 1.11.7.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{1} x^{3} (- 2 i) + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{1 + 3} (- 2 i) + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.7.3

Add $1$ and $3$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 2 i) \cdot 9 + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.8

Multiply $9$ by $- 2$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 2 i) (6 i) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.9

Multiply $x^{3} (- 2 i) (6 i)$ .

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Step 1.11.9.1

Multiply $6$ by $- 2$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 i) i + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.9.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 (i^{1} i)) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.9.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 (i^{1} i^{1})) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.9.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 i^{1 + 1}) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.9.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 i^{2}) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.10

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} (- 12 \cdot - 1) + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.11

Multiply $- 12$ by $- 1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + x^{3} \cdot 12 + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.12

Move $12$ to the left of $x^{3}$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 \cdot x^{3} + 36 x^{2} x + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.13

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.11.13.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 (x \cdot x^{2}) + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.13.2

Multiply $x$ by $x^{2}$ .

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Step 1.11.13.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 (x^{1} x^{2}) + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.13.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{1 + 2} + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.13.3

Add $1$ and $2$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 36 x^{2} \cdot 9 + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.14

Multiply $9$ by $36$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 36 x^{2} (6 i) - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.15

Multiply $6$ by $36$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{2} i x - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.16

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.11.16.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 (x \cdot x^{2}) i - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.16.2

Multiply $x$ by $x^{2}$ .

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Step 1.11.16.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 (x^{1} x^{2}) i - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.16.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{1 + 2} i - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.16.3

Add $1$ and $2$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 16 x^{2} i \cdot 9 - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.17

Multiply $9$ by $- 16$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 16 x^{2} i (6 i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.18

Multiply $- 16 x^{2} i (6 i)$ .

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Step 1.11.18.1

Multiply $6$ by $- 16$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} i i + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.18.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} (i^{1} i) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.18.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} (i^{1} i^{1}) + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.18.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} i^{1 + 1} + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.18.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} i^{2} + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.19

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i - 96 x^{2} \cdot - 1 + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.20

Multiply $- 1$ by $- 96$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x \cdot x + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.21

Multiply $x$ by $x$ by adding the exponents.

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Step 1.11.21.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 (x \cdot x) + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.21.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 36 x \cdot 9 + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.22

Multiply $9$ by $36$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 36 x (6 i) - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.23

Multiply $6$ by $36$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x i x - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.24

Multiply $x$ by $x$ by adding the exponents.

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Step 1.11.24.1

Move $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 (x \cdot x) i - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.24.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 24 x i \cdot 9 - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.25

Multiply $9$ by $- 24$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 24 x i (6 i)) \cdot (x + 9 - 6 i)$

Step 1.11.26

Multiply $- 24 x i (6 i)$ .

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Step 1.11.26.1

Multiply $6$ by $- 24$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x i i) \cdot (x + 9 - 6 i)$

Step 1.11.26.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x (i^{1} i)) \cdot (x + 9 - 6 i)$

Step 1.11.26.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x (i^{1} i^{1})) \cdot (x + 9 - 6 i)$

Step 1.11.26.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x i^{1 + 1}) \cdot (x + 9 - 6 i)$

Step 1.11.26.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x i^{2}) \cdot (x + 9 - 6 i)$

Step 1.11.27

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i - 144 x \cdot - 1) \cdot (x + 9 - 6 i)$

Step 1.11.28

Multiply $- 1$ by $- 144$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.12

Combine the opposite terms in $x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x + 216 x i - 24 x^{2} i - 216 x i + 144 x$ .

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Step 1.12.1

Subtract $216 x i$ from $216 x i$ .

$x = - 3 - 2 i, y = (x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 0 + 144 x) \cdot (x + 9 - 6 i)$

Step 1.12.2

Add $x^{5} + 9 x^{4} + 6 x^{4} i + 11 x^{4} + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i$ and $0$ .

Step 1.13

Add $9 x^{4}$ and $11 x^{4}$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 6 x^{4} i + 99 x^{3} + 66 x^{3} i + x^{4} (- 2 i) + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.14

Add $6 x^{4} i$ and $x^{4} (- 2 i)$ .

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Step 1.14.1

Reorder $x^{4}$ and $- 2$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 99 x^{3} + 66 x^{3} i + 6 x^{4} i - 2 \cdot x^{4} i + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.14.2

Subtract $2 \cdot x^{4} i$ from $6 x^{4} i$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 99 x^{3} + 66 x^{3} i + 4 x^{4} i + x^{3} (- 18 i) + 12 x^{3} + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.15

Add $99 x^{3}$ and $12 x^{3}$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 111 x^{3} + 66 x^{3} i + 4 x^{4} i + x^{3} (- 18 i) + 36 x^{3} + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.16

Add $111 x^{3}$ and $36 x^{3}$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 66 x^{3} i + 4 x^{4} i + x^{3} (- 18 i) + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.17

Add $66 x^{3} i$ and $x^{3} (- 18 i)$ .

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Step 1.17.1

Reorder $x^{3}$ and $- 18$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 66 x^{3} i - 18 \cdot x^{3} i + 4 x^{4} i + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.17.2

Subtract $18 \cdot x^{3} i$ from $66 x^{3} i$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 48 x^{3} i + 4 x^{4} i + 324 x^{2} + 216 x^{2} i - 16 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.18

Subtract $16 x^{3} i$ from $48 x^{3} i$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 324 x^{2} + 216 x^{2} i + 32 x^{3} i - 144 x^{2} i + 96 x^{2} + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.19

Add $324 x^{2}$ and $96 x^{2}$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 420 x^{2} + 216 x^{2} i + 32 x^{3} i - 144 x^{2} i + 36 x^{2} + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.20

Add $420 x^{2}$ and $36 x^{2}$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 456 x^{2} + 216 x^{2} i + 32 x^{3} i - 144 x^{2} i + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.21

Subtract $144 x^{2} i$ from $216 x^{2} i$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 456 x^{2} + 72 x^{2} i + 32 x^{3} i + 324 x - 24 x^{2} i + 144 x) \cdot (x + 9 - 6 i)$

Step 1.22

Subtract $24 x^{2} i$ from $72 x^{2} i$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 456 x^{2} + 48 x^{2} i + 32 x^{3} i + 324 x + 144 x) \cdot (x + 9 - 6 i)$

Step 1.23

Add $324 x$ and $144 x$ .

$x = - 3 - 2 i, y = (x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 456 x^{2} + 48 x^{2} i + 32 x^{3} i + 468 x) \cdot (x + 9 - 6 i)$

Step 1.24

Expand $(x^{5} + 20 x^{4} + 147 x^{3} + 4 x^{4} i + 456 x^{2} + 48 x^{2} i + 32 x^{3} i + 468 x) (x + 9 - 6 i)$ by multiplying each term in the first expression by each term in the second expression.

$x = - 3 - 2 i, y = x^{5} x + x^{5} \cdot 9 + x^{5} (- 6 i) + 20 x^{4} x + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25

Simplify each term.

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Step 1.25.1

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 1.25.1.1

Multiply $x^{5}$ by $x$ .

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Step 1.25.1.1.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{5} x^{1} + x^{5} \cdot 9 + x^{5} (- 6 i) + 20 x^{4} x + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{5 + 1} + x^{5} \cdot 9 + x^{5} (- 6 i) + 20 x^{4} x + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.1.2

Add $5$ and $1$ .

$x = - 3 - 2 i, y = x^{6} + x^{5} \cdot 9 + x^{5} (- 6 i) + 20 x^{4} x + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.2

Move $9$ to the left of $x^{5}$ .

$x = - 3 - 2 i, y = x^{6} + 9 \cdot x^{5} + x^{5} (- 6 i) + 20 x^{4} x + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.3

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 1.25.3.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 (x \cdot x^{4}) + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.3.2

Multiply $x$ by $x^{4}$ .

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Step 1.25.3.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 (x^{1} x^{4}) + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{1 + 4} + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.3.3

Add $1$ and $4$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 20 x^{4} \cdot 9 + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.4

Multiply $9$ by $20$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} + 20 x^{4} (- 6 i) + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.5

Multiply $- 6$ by $20$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{3} x + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.6

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.25.6.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 (x \cdot x^{3}) + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.6.2

Multiply $x$ by $x^{3}$ .

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Step 1.25.6.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 (x^{1} x^{3}) + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{1 + 3} + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.6.3

Add $1$ and $3$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 147 x^{3} \cdot 9 + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.7

Multiply $9$ by $147$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} + 147 x^{3} (- 6 i) + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.8

Multiply $- 6$ by $147$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{4} i x + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.9

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 1.25.9.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 (x \cdot x^{4}) i + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.9.2

Multiply $x$ by $x^{4}$ .

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Step 1.25.9.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 (x^{1} x^{4}) i + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.9.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{1 + 4} i + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.9.3

Add $1$ and $4$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 4 x^{4} i \cdot 9 + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.10

Multiply $9$ by $4$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 4 x^{4} i (- 6 i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.11

Multiply $4 x^{4} i (- 6 i)$ .

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Step 1.25.11.1

Multiply $- 6$ by $4$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} i i + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.11.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} (i^{1} i) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.11.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} (i^{1} i^{1}) + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.11.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} i^{1 + 1} + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.11.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} i^{2} + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.12

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i - 24 x^{4} \cdot - 1 + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.13

Multiply $- 1$ by $- 24$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{2} x + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.14

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.25.14.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 (x \cdot x^{2}) + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.14.2

Multiply $x$ by $x^{2}$ .

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Step 1.25.14.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 (x^{1} x^{2}) + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.14.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{1 + 2} + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.14.3

Add $1$ and $2$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 456 x^{2} \cdot 9 + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.15

Multiply $9$ by $456$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} + 456 x^{2} (- 6 i) + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.16

Multiply $- 6$ by $456$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{2} i x + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.17

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.25.17.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 (x \cdot x^{2}) i + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.17.2

Multiply $x$ by $x^{2}$ .

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Step 1.25.17.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 (x^{1} x^{2}) i + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.17.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{1 + 2} i + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.17.3

Add $1$ and $2$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 48 x^{2} i \cdot 9 + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.18

Multiply $9$ by $48$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 48 x^{2} i (- 6 i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.19

Multiply $48 x^{2} i (- 6 i)$ .

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Step 1.25.19.1

Multiply $- 6$ by $48$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} i i + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.19.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} (i^{1} i) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.19.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} (i^{1} i^{1}) + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.19.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} i^{1 + 1} + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.19.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} i^{2} + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.20

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i - 288 x^{2} \cdot - 1 + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.21

Multiply $- 1$ by $- 288$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{3} i x + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.22

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.25.22.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 (x \cdot x^{3}) i + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.22.2

Multiply $x$ by $x^{3}$ .

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Step 1.25.22.2.1

Raise $x$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 (x^{1} x^{3}) i + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.22.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{1 + 3} i + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.22.3

Add $1$ and $3$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 32 x^{3} i \cdot 9 + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.23

Multiply $9$ by $32$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 32 x^{3} i (- 6 i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.24

Multiply $32 x^{3} i (- 6 i)$ .

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Step 1.25.24.1

Multiply $- 6$ by $32$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} i i + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.24.2

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} (i^{1} i) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.24.3

Raise $i$ to the power of $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} (i^{1} i^{1}) + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.24.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} i^{1 + 1} + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.24.5

Add $1$ and $1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} i^{2} + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.25

Rewrite $i^{2}$ as $- 1$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i - 192 x^{3} \cdot - 1 + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.26

Multiply $- 1$ by $- 192$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x \cdot x + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.27

Multiply $x$ by $x$ by adding the exponents.

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Step 1.25.27.1

Move $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 (x \cdot x) + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.27.2

Multiply $x$ by $x$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 468 x \cdot 9 + 468 x (- 6 i)$

Step 1.25.28

Multiply $9$ by $468$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x + 468 x (- 6 i)$

Step 1.25.29

Multiply $- 6$ by $468$ .

$x = - 3 - 2 i, y = x^{6} + 9 x^{5} + x^{5} (- 6 i) + 20 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.26

Add $9 x^{5}$ and $20 x^{5}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + x^{5} (- 6 i) + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.27

Add $x^{5} (- 6 i)$ and $4 x^{5} i$ .

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Step 1.27.1

Reorder $x^{5}$ and $- 6$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i - 6 \cdot x^{5} i + 4 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.27.2

Add $- 6 \cdot x^{5} i$ and $4 x^{5} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 180 x^{4} - 120 x^{4} i + 147 x^{4} + 1323 x^{3} - 882 x^{3} i - 2 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.28

Add $180 x^{4}$ and $147 x^{4}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 327 x^{4} - 120 x^{4} i + 1323 x^{3} - 882 x^{3} i - 2 x^{5} i + 36 x^{4} i + 24 x^{4} + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.29

Add $327 x^{4}$ and $24 x^{4}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} - 120 x^{4} i + 1323 x^{3} - 882 x^{3} i - 2 x^{5} i + 36 x^{4} i + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.30

Add $- 120 x^{4} i$ and $36 x^{4} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1323 x^{3} - 882 x^{3} i - 2 x^{5} i - 84 x^{4} i + 456 x^{3} + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.31

Add $1323 x^{3}$ and $456 x^{3}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1779 x^{3} - 882 x^{3} i - 2 x^{5} i - 84 x^{4} i + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 192 x^{3} + 468 x^{2} + 4212 x - 2808 x i$

Step 1.32

Add $1779 x^{3}$ and $192 x^{3}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 882 x^{3} i - 2 x^{5} i - 84 x^{4} i + 4104 x^{2} - 2736 x^{2} i + 48 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 468 x^{2} + 4212 x - 2808 x i$

Step 1.33

Add $- 882 x^{3} i$ and $48 x^{3} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i - 84 x^{4} i + 4104 x^{2} - 2736 x^{2} i - 834 x^{3} i + 432 x^{2} i + 288 x^{2} + 32 x^{4} i + 288 x^{3} i + 468 x^{2} + 4212 x - 2808 x i$

Step 1.34

Add $- 84 x^{4} i$ and $32 x^{4} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4104 x^{2} - 2736 x^{2} i - 834 x^{3} i + 432 x^{2} i + 288 x^{2} - 52 x^{4} i + 288 x^{3} i + 468 x^{2} + 4212 x - 2808 x i$

Step 1.35

Add $4104 x^{2}$ and $288 x^{2}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4392 x^{2} - 2736 x^{2} i - 834 x^{3} i + 432 x^{2} i - 52 x^{4} i + 288 x^{3} i + 468 x^{2} + 4212 x - 2808 x i$

Step 1.36

Add $4392 x^{2}$ and $468 x^{2}$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2736 x^{2} i - 834 x^{3} i + 432 x^{2} i - 52 x^{4} i + 288 x^{3} i + 4212 x - 2808 x i$

Step 1.37

Add $- 2736 x^{2} i$ and $432 x^{2} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 834 x^{3} i - 52 x^{4} i + 288 x^{3} i + 4212 x - 2808 x i$

Step 1.38

Add $- 834 x^{3} i$ and $288 x^{3} i$ .

$x = - 3 - 2 i, y = x^{6} + 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2

Move all terms containing variables to the left side of the equation.

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Step 2.1

Subtract $x^{6}$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} = 29 x^{5} + 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.2

Subtract $29 x^{5}$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} = 351 x^{4} + 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.3

Subtract $351 x^{4}$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} = 1971 x^{3} - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.4

Subtract $1971 x^{3}$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} = - 2 x^{5} i + 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.5

Add $2 x^{5} i$ to both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i = 4860 x^{2} - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.6

Subtract $4860 x^{2}$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} = - 2304 x^{2} i - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.7

Add $2304 x^{2} i$ to both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} + 2304 x^{2} i = - 546 x^{3} i - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.8

Add $546 x^{3} i$ to both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} + 2304 x^{2} i + 546 x^{3} i = - 52 x^{4} i + 4212 x - 2808 x i$

Step 2.9

Add $52 x^{4} i$ to both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} + 2304 x^{2} i + 546 x^{3} i + 52 x^{4} i = 4212 x - 2808 x i$

Step 2.10

Subtract $4212 x$ from both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} + 2304 x^{2} i + 546 x^{3} i + 52 x^{4} i - 4212 x = - 2808 x i$

Step 2.11

Add $2808 x i$ to both sides of the equation.

$x = - 3 - 2 i, y - x^{6} - 29 x^{5} - 351 x^{4} - 1971 x^{3} + 2 x^{5} i - 4860 x^{2} + 2304 x^{2} i + 546 x^{3} i + 52 x^{4} i - 4212 x + 2808 x i = 0$

Step 3

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & - 3 - 2 i \\ 2808 i & 1 & 0 \end{array}]$

Step 4

Find the reduced row echelon form.

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Step 4.1

Perform the row operation $R_{2} = R_{2} - 2808 i R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 4.1.1

Perform the row operation $R_{2} = R_{2} - 2808 i R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 3 - 2 i \\ 2808 i - 2808 i \cdot 1 & 1 - 2808 i \cdot 0 & 0 - 2808 i (- 3 - 2 i) \end{array}]$

Step 4.1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 & - 3 - 2 i \\ 0 & 1 & - 5616 + 8424 i \end{array}]$

Step 5

Use the result matrix to declare the final solutions to the system of equations.

$x = - 3 - 2 i$

$y = - 5616 + 8424 i$

Step 6

The solution is the set of ordered pairs that makes the system true.

$(- 3 - 2 i, - 5616 + 8424 i)$

Step 7

Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.

$X = [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 3 - 2 i \\ - 5616 + 8424 i \end{array}]$