Factor 4x^2-36x+81

$4 x^{2} - 36 x + 81$

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

${(2 x)}^{2} - 36 x + 81$

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

${(2 x)}^{2} - 36 x + 9^{2}$

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

$36 x = 2 \cdot (2 x) \cdot 9$

Rewrite the polynomial.

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

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

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