Algebra Examples

$8 a^{4} b^{3} (2 a^{4} b^{5} - 8 a^{3} b) b^{3}$

Step 1

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

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Step 1.1

Move $b^{3}$ .

$8 a^{4} (b^{3} b^{3}) (2 a^{4} b^{5} - 8 a^{3} b)$

Step 1.2

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

$8 a^{4} b^{3 + 3} (2 a^{4} b^{5} - 8 a^{3} b)$

Step 1.3

Add $3$ and $3$ .

$8 a^{4} b^{6} (2 a^{4} b^{5} - 8 a^{3} b)$

Step 2

Apply the distributive property.

$8 a^{4} b^{6} (2 a^{4} b^{5}) + 8 a^{4} b^{6} (- 8 a^{3} b)$

Step 3

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

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Step 3.1

Move $a^{4}$ .

$8 (a^{4} a^{4}) b^{6} (2 b^{5}) + 8 a^{4} b^{6} (- 8 a^{3} b)$

Step 3.2

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

$8 a^{4 + 4} b^{6} (2 b^{5}) + 8 a^{4} b^{6} (- 8 a^{3} b)$

Step 3.3

Add $4$ and $4$ .

$8 a^{8} b^{6} (2 b^{5}) + 8 a^{4} b^{6} (- 8 a^{3} b)$

Step 4

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

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Step 4.1

Move $a^{3}$ .

$8 a^{8} b^{6} (2 b^{5}) + 8 (a^{3} a^{4}) b^{6} (- 8 b)$

Step 4.2

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

$8 a^{8} b^{6} (2 b^{5}) + 8 a^{3 + 4} b^{6} (- 8 b)$

Step 4.3

Add $3$ and $4$ .

$8 a^{8} b^{6} (2 b^{5}) + 8 a^{7} b^{6} (- 8 b)$

Step 5

Simplify each term.

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Step 5.1

Multiply $b^{6}$ by $b^{5}$ by adding the exponents.

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Step 5.1.1

Move $b^{5}$ .

$8 a^{8} (b^{5} b^{6}) \cdot 2 + 8 a^{7} b^{6} (- 8 b)$

Step 5.1.2

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

$8 a^{8} b^{5 + 6} \cdot 2 + 8 a^{7} b^{6} (- 8 b)$

Step 5.1.3

Add $5$ and $6$ .

$8 a^{8} b^{11} \cdot 2 + 8 a^{7} b^{6} (- 8 b)$

Step 5.2

Multiply $2$ by $8$ .

$16 a^{8} b^{11} + 8 a^{7} b^{6} (- 8 b)$

Step 5.3

Multiply $b^{6}$ by $b$ by adding the exponents.

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Step 5.3.1

Move $b$ .

$16 a^{8} b^{11} + 8 a^{7} (b \cdot b^{6}) \cdot - 8$

Step 5.3.2

Multiply $b$ by $b^{6}$ .

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Step 5.3.2.1

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

$16 a^{8} b^{11} + 8 a^{7} (b^{1} b^{6}) \cdot - 8$

Step 5.3.2.2

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

$16 a^{8} b^{11} + 8 a^{7} b^{1 + 6} \cdot - 8$

Step 5.3.3

Add $1$ and $6$ .

$16 a^{8} b^{11} + 8 a^{7} b^{7} \cdot - 8$

Step 5.4

Multiply $- 8$ by $8$ .

$16 a^{8} b^{11} - 64 a^{7} b^{7}$