Factor a^2+14a+49

$a^{2} + 14 a + 49$

Step 1

Rewrite $49$ as $7^{2}$ .

$a^{2} + 14 a + 7^{2}$

Step 2

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

$14 a = 2 \cdot a \cdot 7$

Step 3

Rewrite the polynomial.

$a^{2} + 2 \cdot a \cdot 7 + 7^{2}$

Step 4

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

${(a + 7)}^{2}$