Factor 64a^2-48a+9

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

Step 1

Rewrite $64 a^{2}$ as ${(8 a)}^{2}$ .

${(8 a)}^{2} - 48 a + 9$

Step 2

Rewrite $9$ as $3^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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