Factor 25x^2+20x+4

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

Step 1

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

${(5 x)}^{2} + 20 x + 4$

Step 2

Rewrite $4$ as $2^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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