Algebra Examples

${(6 - 4 x + x^{2})}^{2}$

Step 1

Rewrite ${(6 - 4 x + x^{2})}^{2}$ as $(6 - 4 x + x^{2}) (6 - 4 x + x^{2})$ .

$(6 - 4 x + x^{2}) (6 - 4 x + x^{2})$

Step 2

Expand $(6 - 4 x + x^{2}) (6 - 4 x + x^{2})$ by multiplying each term in the first expression by each term in the second expression.

$6 \cdot 6 + 6 (- 4 x) + 6 x^{2} - 4 x \cdot 6 - 4 x (- 4 x) - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $6$ by $6$ .

$36 + 6 (- 4 x) + 6 x^{2} - 4 x \cdot 6 - 4 x (- 4 x) - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.2

Multiply $- 4$ by $6$ .

$36 - 24 x + 6 x^{2} - 4 x \cdot 6 - 4 x (- 4 x) - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.3

Multiply $6$ by $- 4$ .

$36 - 24 x + 6 x^{2} - 24 x - 4 x (- 4 x) - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$36 - 24 x + 6 x^{2} - 24 x - 4 \cdot - 4 x \cdot x - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.5

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

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Step 3.1.5.1

Move $x$ .

$36 - 24 x + 6 x^{2} - 24 x - 4 \cdot - 4 (x \cdot x) - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.5.2

Multiply $x$ by $x$ .

$36 - 24 x + 6 x^{2} - 24 x - 4 \cdot - 4 x^{2} - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.6

Multiply $- 4$ by $- 4$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x \cdot x^{2} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.7

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

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Step 3.1.7.1

Move $x^{2}$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 (x^{2} x) + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.7.2

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

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Step 3.1.7.2.1

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 (x^{2} x^{1}) + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.7.2.2

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{2 + 1} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.7.3

Add $2$ and $1$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + x^{2} \cdot 6 + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.8

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 \cdot x^{2} + x^{2} (- 4 x) + x^{2} x^{2}$

Step 3.1.9

Rewrite using the commutative property of multiplication.

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{2} x + x^{2} x^{2}$

Step 3.1.10

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

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Step 3.1.10.1

Move $x$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 (x \cdot x^{2}) + x^{2} x^{2}$

Step 3.1.10.2

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

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Step 3.1.10.2.1

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 (x^{1} x^{2}) + x^{2} x^{2}$

Step 3.1.10.2.2

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{1 + 2} + x^{2} x^{2}$

Step 3.1.10.3

Add $1$ and $2$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{3} + x^{2} x^{2}$

Step 3.1.11

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

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Step 3.1.11.1

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

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{3} + x^{2 + 2}$

Step 3.1.11.2

Add $2$ and $2$ .

$36 - 24 x + 6 x^{2} - 24 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{3} + x^{4}$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

Subtract $24 x$ from $- 24 x$ .

$36 + 6 x^{2} - 48 x + 16 x^{2} - 4 x^{3} + 6 x^{2} - 4 x^{3} + x^{4}$

Step 3.2.2

Add $6 x^{2}$ and $16 x^{2}$ .

$36 + 22 x^{2} - 48 x - 4 x^{3} + 6 x^{2} - 4 x^{3} + x^{4}$

Step 3.2.3

Add $22 x^{2}$ and $6 x^{2}$ .

$36 + 28 x^{2} - 48 x - 4 x^{3} - 4 x^{3} + x^{4}$

Step 3.2.4

Subtract $4 x^{3}$ from $- 4 x^{3}$ .

$36 + 28 x^{2} - 48 x - 8 x^{3} + x^{4}$

Step 3.2.5

Simplify the expression.

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Step 3.2.5.1

Move $36$ .

$28 x^{2} - 48 x - 8 x^{3} + x^{4} + 36$

Step 3.2.5.2

Move $- 48 x$ .

$28 x^{2} - 8 x^{3} + x^{4} - 48 x + 36$

Step 3.2.5.3

Move $28 x^{2}$ .

$- 8 x^{3} + x^{4} + 28 x^{2} - 48 x + 36$

Step 3.2.5.4

Reorder $- 8 x^{3}$ and $x^{4}$ .

$x^{4} - 8 x^{3} + 28 x^{2} - 48 x + 36$