Factor 25a^2+20a+4

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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