Algebra Examples

$121 a^{2} b^{3} - 169 b^{2} b^{3}$

Step 1

Factor $b^{2}$ out of $121 a^{2} b^{3} - 169 b^{2} b^{3}$ .

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Step 1.1

Factor $b^{2}$ out of $121 a^{2} b^{3}$ .

$b^{2} (121 a^{2} b) - 169 b^{2} b^{3}$

Step 1.2

Factor $b^{2}$ out of $- 169 b^{2} b^{3}$ .

$b^{2} (121 a^{2} b) + b^{2} (- 169 b^{3})$

Step 1.3

Factor $b^{2}$ out of $b^{2} (121 a^{2} b) + b^{2} (- 169 b^{3})$ .

$b^{2} (121 a^{2} b - 169 b^{3})$

Step 2

Factor $b$ out of $121 a^{2} b - 169 b^{3}$ .

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Step 2.1

Factor $b$ out of $121 a^{2} b$ .

$b^{2} (b (121 a^{2}) - 169 b^{3})$

Step 2.2

Factor $b$ out of $- 169 b^{3}$ .

$b^{2} (b (121 a^{2}) + b (- 169 b^{2}))$

Step 2.3

Factor $b$ out of $b (121 a^{2}) + b (- 169 b^{2})$ .

$b^{2} (b (121 a^{2} - 169 b^{2}))$

Step 3

Rewrite $121 a^{2}$ as ${(11 a)}^{2}$ .

$b^{2} (b ({(11 a)}^{2} - 169 b^{2}))$

Step 4

Rewrite $169 b^{2}$ as ${(13 b)}^{2}$ .

$b^{2} (b ({(11 a)}^{2} - {(13 b)}^{2}))$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 11 a$ and $b = 13 b$ .

$b^{2} (b ((11 a + 13 b) (11 a - (13 b))))$

Step 6

Factor.

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Step 6.1

Factor.

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Step 6.1.1

Multiply $13$ by $- 1$ .

$b^{2} (b ((11 a + 13 b) (11 a - 13 b)))$

Step 6.1.2

Remove unnecessary parentheses.

$b^{2} (b (11 a + 13 b) (11 a - 13 b))$

Step 6.2

Remove unnecessary parentheses.

$b^{2} b (11 a + 13 b) (11 a - 13 b)$

Step 7

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

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Step 7.1

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

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Step 7.1.1

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

$b^{2} b^{1} (11 a + 13 b) (11 a - 13 b)$

Step 7.1.2

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

$b^{2 + 1} (11 a + 13 b) (11 a - 13 b)$

Step 7.2

Add $2$ and $1$ .

$b^{3} (11 a + 13 b) (11 a - 13 b)$