Factor 16+40x+25x^2

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

Step 1

Rewrite $16$ as $4^{2}$ .

$4^{2} + 40 x + 25 x^{2}$

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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