Factor 18x^3-200xy^2

$18 x^{3} - 200 x y^{2}$

Step 1

Factor $2 x$ out of $18 x^{3} - 200 x y^{2}$ .

Factor $2 x$ out of $18 x^{3}$ .

$2 x (9 x^{2}) - 200 x y^{2}$

Factor $2 x$ out of $- 200 x y^{2}$ .

$2 x (9 x^{2}) + 2 x (- 100 y^{2})$

Factor $2 x$ out of $2 x (9 x^{2}) + 2 x (- 100 y^{2})$ .

$2 x (9 x^{2} - 100 y^{2})$

Step 2

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

$2 x ({(3 x)}^{2} - 100 y^{2})$

Step 3

Rewrite $100 y^{2}$ as ${(10 y)}^{2}$ .

$2 x ({(3 x)}^{2} - {(10 y)}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 10 y$ .

$2 x ((3 x + 10 y) (3 x - (10 y)))$

Step 5

Factor.

Multiply $10$ by $- 1$ .

$2 x ((3 x + 10 y) (3 x - 10 y))$

Remove unnecessary parentheses.

$2 x (3 x + 10 y) (3 x - 10 y)$

Factor 18x^3-200xy^2

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