Factor 81x^2-90x+25

$81 x^{2} - 90 x + 25$

Step 1

Rewrite $81 x^{2}$ as ${(9 x)}^{2}$ .

${(9 x)}^{2} - 90 x + 25$

Step 2

Rewrite $25$ as $5^{2}$ .

${(9 x)}^{2} - 90 x + 5^{2}$

Step 3

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

$90 x = 2 \cdot (9 x) \cdot 5$

Step 4

Rewrite the polynomial.

${(9 x)}^{2} - 2 \cdot (9 x) \cdot 5 + 5^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 9 x$ and $b = 5$ .

${(9 x - 5)}^{2}$