Algebra Examples

$9 a^{2} b^{4} - 16 b^{2} c^{6}$

Step 1

Factor out the GCF of $b^{2}$ from $9 a^{2} b^{4} - 16 b^{2} c^{6}$ .

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Step 1.1

Factor out the GCF of $b^{2}$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $b^{2}$ from the expression $9 a^{2} b^{4}$ .

$b^{2} (9 a^{2} b^{2}) - 16 b^{2} c^{6}$

Step 1.1.2

Factor out the GCF of $b^{2}$ from the expression $- 16 b^{2} c^{6}$ .

$b^{2} (9 a^{2} b^{2}) + b^{2} (- 16 c^{6})$

Step 1.2

Since all the terms share a common factor of $b^{2}$ , it can be factored out of each term.

$b^{2} (9 a^{2} b^{2} - 16 c^{6})$

Step 2

Rewrite $9 a^{2} b^{2}$ as ${(3 a b)}^{2}$ .

$b^{2} ({(3 a b)}^{2} - 16 c^{6})$

Step 3

Rewrite $16 c^{6}$ as ${(4 c^{3})}^{2}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a b$ and $b = 4 c^{3}$ .

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

Step 5

Multiply $4$ by $- 1$ .

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