Factor 50u^2vw-162v^3w

$50 u^{2} v w - 162 v^{3} w$

Step 1

Factor $2 v w$ out of $50 u^{2} v w - 162 v^{3} w$ .

Factor $2 v w$ out of $50 u^{2} v w$ .

$2 v w (25 u^{2}) - 162 v^{3} w$

Factor $2 v w$ out of $- 162 v^{3} w$ .

$2 v w (25 u^{2}) + 2 v w (- 81 v^{2})$

Factor $2 v w$ out of $2 v w (25 u^{2}) + 2 v w (- 81 v^{2})$ .

$2 v w (25 u^{2} - 81 v^{2})$

Step 2

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

$2 v w ({(5 u)}^{2} - 81 v^{2})$

Step 3

Rewrite $81 v^{2}$ as ${(9 v)}^{2}$ .

$2 v w ({(5 u)}^{2} - {(9 v)}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 u$ and $b = 9 v$ .

$2 v w ((5 u + 9 v) (5 u - (9 v)))$

Step 5

Factor.

Multiply $9$ by $- 1$ .

$2 v w ((5 u + 9 v) (5 u - 9 v))$

Remove unnecessary parentheses.

$2 v w (5 u + 9 v) (5 u - 9 v)$

Factor 50u^2vw-162v^3w

Related Questions

Support LCMGCF.com by disabling your adblocker.