Factor 9w^2-48w+64

$9 w^{2} - 48 w + 64$

Step 1

Rewrite $9 w^{2}$ as ${(3 w)}^{2}$ .

${(3 w)}^{2} - 48 w + 64$

Step 2

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

${(3 w)}^{2} - 48 w + 8^{2}$

Step 3

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

$48 w = 2 \cdot (3 w) \cdot 8$

Step 4

Rewrite the polynomial.

${(3 w)}^{2} - 2 \cdot (3 w) \cdot 8 + 8^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 w$ and $b = 8$ .

${(3 w - 8)}^{2}$