Factor 25x^2+100-100x

$25 x^{2} + 100 - 100 x$

Step 1

Factor $25$ out of $25 x^{2} + 100 - 100 x$ .

Factor $25$ out of $25 x^{2}$ .

$25 (x^{2}) + 100 - 100 x$

Factor $25$ out of $100$ .

$25 x^{2} + 25 \cdot 4 - 100 x$

Factor $25$ out of $- 100 x$ .

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

Factor $25$ out of $25 x^{2} + 25 \cdot 4$ .

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

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

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

Step 2

Factor using the perfect square rule.

Rearrange terms.

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

Rewrite $4$ as $2^{2}$ .

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

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

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

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

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

$25 {(x - 2)}^{2}$