Factor 4x^2+20xy+25y^2

$4 x^{2} + 20 x y + 25 y^{2}$

Step 1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

${(2 x)}^{2} + 20 x y + 25 y^{2}$

Step 2

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

${(2 x)}^{2} + 20 x y + {(5 y)}^{2}$

Step 3

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

$20 x y = 2 \cdot (2 x) \cdot (5 y)$

Step 4

Rewrite the polynomial.

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

Step 5

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

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