Factor y^2+12y+36

Problem

y2+12*y+36

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y2+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 y2 is (y)2 the last term 36 is (6)2 and the middle term 12*y is 2*(y)*(6)

3. Apply the formula for a perfect square trinomial, which states a2+2*a*b+b2=(a+b)2

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

Final Answer

y2+12*y+36=(y+6)2

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