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Factor. $\newline$ $x^2 - 2x + 1$

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Factor quadratics: special cases

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Q. Factor.

\newline

x^2 - 2x + 1

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ . We need to check if $x^2 - 2x + 1$ fits this pattern.
Identify $a$ and $b$ : Identify the values of $a$ and $b$ that would make $x^2 - 2x + 1$ a perfect square trinomial. $\newline$ For $x^2 - 2x + 1$ , $a = x$ and $b = 1$ because $(x)^2 = x^2$ and $(1)^2 = 1$ . The middle term $b$ $0$ should be equal to $b$ $1$ , which is $b$ $2$ . This matches the middle term of our expression.
Write Factored Form: Write the factored form using the values of $a$ and $b$ . Since the expression fits the pattern of a perfect square trinomial, we can write it as $(a - b)^2$ . Therefore, $x^2 - 2x + 1 = (x - 1)^2$ .

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