Factor x^2y^2-20xy+100

$x^{2} y^{2} - 20 x y + 100$

Step 1

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

${(x y)}^{2} - 20 (x y) + 100$

Step 2

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$u^{2} - 20 u + 100$

Step 3

Factor using the perfect square rule.

Rewrite $100$ as $10^{2}$ .

$u^{2} - 20 u + 10^{2}$

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

$20 u = 2 \cdot u \cdot 10$

Rewrite the polynomial.

$u^{2} - 2 \cdot u \cdot 10 + 10^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = u$ and $b = 10$ .

${(u - 10)}^{2}$

Step 4

Replace all occurrences of $u$ with $x y$ .

${(x y - 10)}^{2}$