Factor 16a^2+40a+25

$16 a^{2} + 40 a + 25$

Step 1

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

${(4 a)}^{2} + 40 a + 25$

Step 2

Rewrite $25$ as $5^{2}$ .

${(4 a)}^{2} + 40 a + 5^{2}$

Step 3

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

$40 a = 2 \cdot (4 a) \cdot 5$

Step 4

Rewrite the polynomial.

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

Step 5

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

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