Factor as the product of two binomials. x^(2)-2x+1=

Recognize as perfect square trinomial: Recognize the quadratic expression x^2 - 2x + 1 as a perfect square trinomial. A perfect square trinomial is in the form (a - b)^2 = a^2 - 2ab + b^2, where a is the square root of the first term and b is the square root of the last term.Identify values of a and b: Identify the values of a and b that will satisfy the equation (a - b)^2 = x^2 - 2x + 1. For the given expression, a = x and b = 1 because x^2 is the square of x and 1 is the square of 1.Write factored form: Write the factored form using the values of a and b. The factored form is (x - 1)(x - 1) or (x - 1)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor as the product of two binomials.

\newline

x^{2}-2x+1=

Recognize as perfect square trinomial: Recognize the quadratic expression $x^2 - 2x + 1$ as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ , where $a$ is the square root of the first term and $b$ is the square root of the last term.
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ that will satisfy the equation $(a - b)^2 = x^2 - 2x + 1$ . $\newline$ For the given expression, $a = x$ and $b = 1$ because $x^2$ is the square of $x$ and $1$ is the square of $1$ .
Write factored form: Write the factored form using the values of $a$ and $b$ . $\newline$ The factored form is $(x - 1)(x - 1)$ or $(x - 1)^2$ .