Factor 100w^2x^2-64y^2z^2

$100 w^{2} x^{2} - 64 y^{2} z^{2}$

Step 1

Factor $4$ out of $100 w^{2} x^{2} - 64 y^{2} z^{2}$ .

Factor $4$ out of $100 w^{2} x^{2}$ .

$4 (25 w^{2} x^{2}) - 64 y^{2} z^{2}$

Factor $4$ out of $- 64 y^{2} z^{2}$ .

$4 (25 w^{2} x^{2}) + 4 (- 16 y^{2} z^{2})$

Factor $4$ out of $4 (25 w^{2} x^{2}) + 4 (- 16 y^{2} z^{2})$ .

$4 (25 w^{2} x^{2} - 16 y^{2} z^{2})$

Step 2

Rewrite $25 w^{2} x^{2}$ as ${(5 w x)}^{2}$ .

$4 ({(5 w x)}^{2} - 16 y^{2} z^{2})$

Step 3

Rewrite $16 y^{2} z^{2}$ as ${(4 y z)}^{2}$ .

$4 ({(5 w x)}^{2} - {(4 y z)}^{2})$

Step 4

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

$4 ((5 w x + 4 y z) (5 w x - (4 y z)))$

Step 5

Factor.

Simplify.

Multiply $4$ by $- 1$ .

$4 ((5 w x + 4 y z) (5 w x - 4 (y z)))$

Remove parentheses.

$4 ((5 w x + 4 y z) (5 w x - 4 y z))$

Remove unnecessary parentheses.

$4 (5 w x + 4 y z) (5 w x - 4 y z)$

Factor 100w^2x^2-64y^2z^2

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