Algebra Examples

$100 x^{4} y^{8} - 144 a^{6}$

Step 1

Factor $4$ out of $100 x^{4} y^{8} - 144 a^{6}$ .

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Step 1.1

Factor $4$ out of $100 x^{4} y^{8}$ .

$4 (25 x^{4} y^{8}) - 144 a^{6}$

Step 1.2

Factor $4$ out of $- 144 a^{6}$ .

$4 (25 x^{4} y^{8}) + 4 (- 36 a^{6})$

Step 1.3

Factor $4$ out of $4 (25 x^{4} y^{8}) + 4 (- 36 a^{6})$ .

$4 (25 x^{4} y^{8} - 36 a^{6})$

Step 2

Rewrite $25 x^{4} y^{8}$ as ${(5 x^{2} y^{4})}^{2}$ .

$4 ({(5 x^{2} y^{4})}^{2} - 36 a^{6})$

Step 3

Rewrite $36 a^{6}$ as ${(6 a^{3})}^{2}$ .

$4 ({(5 x^{2} y^{4})}^{2} - {(6 a^{3})}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x^{2} y^{4}$ and $b = 6 a^{3}$ .

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

Step 5

Factor.

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Step 5.1

Multiply $6$ by $- 1$ .

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

Step 5.2

Remove unnecessary parentheses.

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