Factor v^2-10v+25

Problem

v^2−10*v+25

Solution

1. Identify the structure of the quadratic expression, which is in the form a*v^2+b*v+c where a=1 b=−10 and c=25

2. Recognize that the expression is a perfect square trinomial because the first term is v^2 the last term is 5^2 and the middle term is −2*(v)*(5)

3. Apply the formula for a perfect square trinomial, a^2−2*a*b+b^2=(a−b)^2

4. Substitute a=v and b=5 into the binomial square form.

Final Answer

v^2−10*v+25=(v−5)^2

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