Factor y^2-12y+36

Problem

y^2−12*y+36

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y^2+b*y+c where a=1 b=−12 and c=36

2. Recognize that the expression is a perfect square trinomial because the first term is y^2 the last term is 6^2 and the middle term is −2*(y)*(6)

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

4. Substitute a=y and b=6 into the binomial square form.

Final Answer

y^2−12*y+36=(y−6)^2

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