Factor 16x^2-72x+81

$16 x^{2} - 72 x + 81$

Step 1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

${(4 x)}^{2} - 72 x + 81$

Step 2

Rewrite $81$ as $9^{2}$ .

${(4 x)}^{2} - 72 x + 9^{2}$

Step 3

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

$72 x = 2 \cdot (4 x) \cdot 9$

Step 4

Rewrite the polynomial.

${(4 x)}^{2} - 2 \cdot (4 x) \cdot 9 + 9^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 4 x$ and $b = 9$ .

${(4 x - 9)}^{2}$