Factor x^2+6xy+9y^2

Problem

x^2+6*x*y+9*y^2

Solution

1. Identify the structure of the expression as a trinomial of the form a^2+2*a*b+b^2

2. Determine the square roots of the first and last terms, where a^2=x^2 and b^2=9*y^2

3. Calculate the values of a and b to be a=x and b=3*y

4. Verify the middle term by checking if 2*a*b equals 6*x*y

2*(x)*(3*y)=6*x*y

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

Final Answer

x^2+6*x*y+9*y^2=(x+3*y)^2

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