Factor x^2+12x+36

Problem

x^2+12*x+36

Solution

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

2. Recognize that the expression is a perfect square trinomial because the first term is x^2 the last term is 6^2 and the middle term is 2⋅x⋅6

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

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

Final Answer

x^2+12*x+36=(x+6)^2

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