Factor. v^2 - 2v + 1 ______

Determine Approach: Determine the approach to factor v^2 - 2v + 1. This expression is a perfect square trinomial because it can be written in the form (a - b)^2 where a^2 = v^2, 2ab = 2v, and b^2 = 1.Identify Values: Identify the values of a and b that satisfy the equation (a - b)^2 = a^2 - 2ab + b^2. For the given expression, a = v and b = 1 because v^2 = (v)^2 and 1 = (1)^2.Write Factored Form: Write the factored form using the values of a and b. The factored form is (v - 1)(v - 1) or (v - 1)^2.

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

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

\newline

v^2 - 2v + 1

Determine Approach: Determine the approach to factor $v^2 - 2v + 1$ . This expression is a perfect square trinomial because it can be written in the form $(a - b)^2$ where $a^2 = v^2$ , $2ab = 2v$ , and $b^2 = 1$ .
Identify Values: Identify the values of $a$ and $b$ that satisfy the equation $(a - b)^2 = a^2 - 2ab + b^2$ . For the given expression, $a = v$ and $b = 1$ because $v^2 = (v)^2$ and $1 = (1)^2$ .
Write Factored Form: Write the factored form using the values of $a$ and $b$ . The factored form is $(v - 1)(v - 1)$ or $(v - 1)^2$ .