Factor 4-4x+x^2

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

Step 1

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

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

Step 2

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

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

Step 3

Rewrite the polynomial.

$2^{2} - 2 \cdot 2 \cdot x + x^{2}$

Step 4

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

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