Factor 14x^2-224y^2

$14 x^{2} - 224 y^{2}$

Step 1

Factor $14$ out of $14 x^{2} - 224 y^{2}$ .

Factor $14$ out of $14 x^{2}$ .

$14 (x^{2}) - 224 y^{2}$

Factor $14$ out of $- 224 y^{2}$ .

$14 (x^{2}) + 14 (- 16 y^{2})$

Factor $14$ out of $14 (x^{2}) + 14 (- 16 y^{2})$ .

$14 (x^{2} - 16 y^{2})$

Step 2

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

$14 (x^{2} - {(4 y)}^{2})$

Step 3

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

$14 ((x + 4 y) (x - (4 y)))$

Step 4

Factor.

Multiply $4$ by $- 1$ .

$14 ((x + 4 y) (x - 4 y))$

Remove unnecessary parentheses.

$14 (x + 4 y) (x - 4 y)$