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

Problem

x2+6*x*y+9*y2

Solution

1. Identify the structure of the expression as a trinomial of the form a2+2*a*b+b2

2. Determine the square roots of the first and last terms, where a2=x2 and b2=9*y2

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 a2+2*a*b+b2=(a+b)2

Final Answer

x2+6*x*y+9*y2=(x+3*y)2

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