Algebra Examples

$9 x^{4} (x^{3} - 6 x) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 x^{4} x^{3} + 9 x^{4} (- 6 x) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.2

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 1.2.1

Move $x^{3}$ .

$9 (x^{3} x^{4}) + 9 x^{4} (- 6 x) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.2.2

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

$9 x^{3 + 4} + 9 x^{4} (- 6 x) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.2.3

Add $3$ and $4$ .

$9 x^{7} + 9 x^{4} (- 6 x) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.3

Rewrite using the commutative property of multiplication.

$9 x^{7} + 9 \cdot - 6 x^{4} x + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x$ .

$9 x^{7} + 9 \cdot - 6 (x \cdot x^{4}) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$9 x^{7} + 9 \cdot - 6 (x^{1} x^{4}) + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.4.1.2.2

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

$9 x^{7} + 9 \cdot - 6 x^{1 + 4} + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.4.1.3

Add $1$ and $4$ .

$9 x^{7} + 9 \cdot - 6 x^{5} + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.4.2

Multiply $9$ by $- 6$ .

$9 x^{7} - 54 x^{5} + 4 x^{2} (6 x^{5} + 5 x^{3})$

Step 1.5

Apply the distributive property.

$9 x^{7} - 54 x^{5} + 4 x^{2} (6 x^{5}) + 4 x^{2} (5 x^{3})$

Step 1.6

Rewrite using the commutative property of multiplication.

$9 x^{7} - 54 x^{5} + 4 \cdot 6 x^{2} x^{5} + 4 x^{2} (5 x^{3})$

Step 1.7

Rewrite using the commutative property of multiplication.

$9 x^{7} - 54 x^{5} + 4 \cdot 6 x^{2} x^{5} + 4 \cdot 5 x^{2} x^{3}$

Step 1.8

Simplify each term.

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Step 1.8.1

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 1.8.1.1

Move $x^{5}$ .

$9 x^{7} - 54 x^{5} + 4 \cdot 6 (x^{5} x^{2}) + 4 \cdot 5 x^{2} x^{3}$

Step 1.8.1.2

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

$9 x^{7} - 54 x^{5} + 4 \cdot 6 x^{5 + 2} + 4 \cdot 5 x^{2} x^{3}$

Step 1.8.1.3

Add $5$ and $2$ .

$9 x^{7} - 54 x^{5} + 4 \cdot 6 x^{7} + 4 \cdot 5 x^{2} x^{3}$

Step 1.8.2

Multiply $4$ by $6$ .

$9 x^{7} - 54 x^{5} + 24 x^{7} + 4 \cdot 5 x^{2} x^{3}$

Step 1.8.3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.8.3.1

Move $x^{3}$ .

$9 x^{7} - 54 x^{5} + 24 x^{7} + 4 \cdot 5 (x^{3} x^{2})$

Step 1.8.3.2

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

$9 x^{7} - 54 x^{5} + 24 x^{7} + 4 \cdot 5 x^{3 + 2}$

Step 1.8.3.3

Add $3$ and $2$ .

$9 x^{7} - 54 x^{5} + 24 x^{7} + 4 \cdot 5 x^{5}$

Step 1.8.4

Multiply $4$ by $5$ .

$9 x^{7} - 54 x^{5} + 24 x^{7} + 20 x^{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $9 x^{7}$ and $24 x^{7}$ .

$33 x^{7} - 54 x^{5} + 20 x^{5}$

Step 2.2

Add $- 54 x^{5}$ and $20 x^{5}$ .

$33 x^{7} - 34 x^{5}$