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

Problem

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

Solution

1. Identify the structure of the expression as a quadratic trinomial in terms of y and x

2. Recognize that the first term y^2 is the square of y and the last term 9*x^2 is the square of 3*x

3. Check if the middle term 6*x*y fits the pattern 2*a*b for a perfect square trinomial (a+b)^2=a^2+2*a*b+b^2

4. Verify the middle term by calculating $2(y)(3x) = 6xy$, which matches the given expression.

5. Apply the perfect square trinomial formula where a=y and b=3*x

Final Answer

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

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