Factor. c^2 - 2c + 1 ______

Determine Approach: Determine the approach to factor the quadratic expression c^2 - 2c + 1. This is a perfect square trinomial because it can be written in the form (a - b)^2 where a^2 is the first term, -2ab is the middle term, and b^2 is the last term.Identify Values: Identify the values of a and b that will satisfy the equation (a - b)^2 = a^2 - 2ab + b^2 for the given expression c^2 - 2c + 1. Here, a^2 = c^2, which means a = c. To find b, we look at the last term, b^2 = 1, which means b = 1.Write Factored Form: Write the factored form using the values of a and b. The factored form is (a - b)^2 = (c - 1)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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c^2 - 2c + 1

Determine Approach: Determine the approach to factor the quadratic expression $c^2 - 2c + 1$ . This is a perfect square trinomial because it can be written in the form $(a - b)^2$ where $a^2$ is the first term, $-2ab$ is the middle term, and $b^2$ is the last term.
Identify Values: Identify the values of $a$ and $b$ that will satisfy the equation $(a - b)^2 = a^2 - 2ab + b^2$ for the given expression $c^2 - 2c + 1$ . Here, $a^2 = c^2$ , which means $a = c$ . To find $b$ , we look at the last term, $b^2 = 1$ , which means $b = 1$ .
Write Factored Form: Write the factored form using the values of $a$ and $b$ . The factored form is $(a - b)^2 = (c - 1)^2$ .