Factor 90x^3y+480x^2y^2+640xy^3

$90 x^{3} y + 480 x^{2} y^{2} + 640 x y^{3}$

Step 1

Factor $10 x y$ out of $90 x^{3} y + 480 x^{2} y^{2} + 640 x y^{3}$ .

Factor $10 x y$ out of $90 x^{3} y$ .

$10 x y (9 x^{2}) + 480 x^{2} y^{2} + 640 x y^{3}$

Factor $10 x y$ out of $480 x^{2} y^{2}$ .

$10 x y (9 x^{2}) + 10 x y (48 x y) + 640 x y^{3}$

Factor $10 x y$ out of $640 x y^{3}$ .

$10 x y (9 x^{2}) + 10 x y (48 x y) + 10 x y (64 y^{2})$

Factor $10 x y$ out of $10 x y (9 x^{2}) + 10 x y (48 x y)$ .

$10 x y (9 x^{2} + 48 x y) + 10 x y (64 y^{2})$

Factor $10 x y$ out of $10 x y (9 x^{2} + 48 x y) + 10 x y (64 y^{2})$ .

$10 x y (9 x^{2} + 48 x y + 64 y^{2})$

Step 2

Factor using the perfect square rule.

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

$10 x y ({(3 x)}^{2} + 48 x y + 64 y^{2})$

Rewrite $64 y^{2}$ as ${(8 y)}^{2}$ .

$10 x y ({(3 x)}^{2} + 48 x y + {(8 y)}^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$48 x y = 2 \cdot (3 x) \cdot (8 y)$

Rewrite the polynomial.

$10 x y ({(3 x)}^{2} + 2 \cdot (3 x) \cdot (8 y) + {(8 y)}^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3 x$ and $b = 8 y$ .

$10 x y {(3 x + 8 y)}^{2}$