Factor x^2+12x+36-9y^2

Problem

x^2+12*x+36−9*y^2

Solution

1. Group the first three terms to identify a potential perfect square trinomial.

x^2+12*x+36−9*y^2=(x^2+12*x+36)−9*y^2

2. Factor the perfect square trinomial (x^2+12*x+36) by recognizing it follows the pattern a^2+2*a*b+b^2=(a+b)^2

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

3. Rewrite the expression using the factored trinomial and express the last term as a perfect square.

(x+6)^2−(3*y)^2

4. Apply the formula for the difference of squares, a^2−b^2=(a−b)*(a+b) where a=x+6 and b=3*y

(x+6−3*y)*(x+6+3*y)

Final Answer

x^2+12*x+36−9*y^2=(x−3*y+6)*(x+3*y+6)

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