Factor 4x^2-40x+100

$4 x^{2} - 40 x + 100$

Step 1

Factor $4$ out of $4 x^{2} - 40 x + 100$ .

Factor $4$ out of $4 x^{2}$ .

$4 (x^{2}) - 40 x + 100$

Factor $4$ out of $- 40 x$ .

$4 (x^{2}) + 4 (- 10 x) + 100$

Factor $4$ out of $100$ .

$4 x^{2} + 4 (- 10 x) + 4 \cdot 25$

Factor $4$ out of $4 x^{2} + 4 (- 10 x)$ .

$4 (x^{2} - 10 x) + 4 \cdot 25$

Factor $4$ out of $4 (x^{2} - 10 x) + 4 \cdot 25$ .

$4 (x^{2} - 10 x + 25)$

Step 2

Factor using the perfect square rule.

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

$4 (x^{2} - 10 x + 5^{2})$

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

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$4 (x^{2} - 2 \cdot x \cdot 5 + 5^{2})$

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

$4 {(x - 5)}^{2}$