Factor. 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. For x^2 - 2x + 1, a = x and b = 1 because (x)^2 = x^2 and (1)^2 = 1. The middle term -2x should be equal to -2ab, which is -2(x)(1) = -2x. 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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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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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, $x^2 - 2x + 1 = (x - 1)^2$ .