Factor 25x^2+40xy+16y^2

$25 x^{2} + 40 x y + 16 y^{2}$

Step 1

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

${(5 x)}^{2} + 40 x y + 16 y^{2}$

Step 2

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

${(5 x)}^{2} + 40 x y + {(4 y)}^{2}$

Step 3

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

$40 x y = 2 \cdot (5 x) \cdot (4 y)$

Step 4

Rewrite the polynomial.

${(5 x)}^{2} + 2 \cdot (5 x) \cdot (4 y) + {(4 y)}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 x$ and $b = 4 y$ .

${(5 x + 4 y)}^{2}$