Factor x^2-2x+1

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Algebra

Factor x^2-2x+1

$x^{2} - 2 x + 1$

Rewrite $1$ as $1^{2}$ .

$x^{2} - 2 x + 1^{2}$

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

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 1 + 1^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

${(x - 1)}^{2}$

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