Factor 49x^2+112x+64

$49 x^{2} + 112 x + 64$

Step 1

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

${(7 x)}^{2} + 112 x + 64$

Step 2

Rewrite $64$ as $8^{2}$ .

${(7 x)}^{2} + 112 x + 8^{2}$

Step 3

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

$112 x = 2 \cdot (7 x) \cdot 8$

Step 4

Rewrite the polynomial.

${(7 x)}^{2} + 2 \cdot (7 x) \cdot 8 + 8^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 7 x$ and $b = 8$ .

${(7 x + 8)}^{2}$