Factor 49n^2-56n+16

$49 n^{2} - 56 n + 16$

Step 1

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

${(7 n)}^{2} - 56 n + 16$

Step 2

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

${(7 n)}^{2} - 56 n + 4^{2}$

Step 3

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

$56 n = 2 \cdot (7 n) \cdot 4$

Step 4

Rewrite the polynomial.

${(7 n)}^{2} - 2 \cdot (7 n) \cdot 4 + 4^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 7 n$ and $b = 4$ .

${(7 n - 4)}^{2}$