Factor 4x^2+12xy+9y^2

Problem

4*x^2+12*x*y+9*y^2

Solution

1. Identify the structure of the expression as a trinomial that may be a perfect square trinomial of the form a^2+2*a*b+b^2

2. Determine the square root of the first term, 4*x^2 which is 2*x

3. Determine the square root of the last term, 9*y^2 which is 3*y

4. Verify the middle term by calculating 2*(2*x)*(3*y) which equals 12*x*y

5. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2 where a=2*x and b=3*y

Final Answer

4*x^2+12*x*y+9*y^2=(2*x+3*y)^2

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