Factor 7x^2-28x+28

$7 x^{2} - 28 x + 28$

Step 1

Factor $7$ out of $7 x^{2} - 28 x + 28$ .

Factor $7$ out of $7 x^{2}$ .

$7 (x^{2}) - 28 x + 28$

Factor $7$ out of $- 28 x$ .

$7 (x^{2}) + 7 (- 4 x) + 28$

Factor $7$ out of $28$ .

$7 x^{2} + 7 (- 4 x) + 7 \cdot 4$

Factor $7$ out of $7 x^{2} + 7 (- 4 x)$ .

$7 (x^{2} - 4 x) + 7 \cdot 4$

Factor $7$ out of $7 (x^{2} - 4 x) + 7 \cdot 4$ .

$7 (x^{2} - 4 x + 4)$

Step 2

Factor using the perfect square rule.

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

$7 (x^{2} - 4 x + 2^{2})$

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.

$7 (x^{2} - 2 \cdot x \cdot 2 + 2^{2})$

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

$7 {(x - 2)}^{2}$