Factor y^2+6y+9

Problem

y^2+6*y+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y^2+b*y+c where a=1 b=6 and c=9

2. Recognize that the expression is a perfect square trinomial because the first term is y^2 the last term is 3^2 and the middle term is 2⋅y⋅3

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

4. Substitute a=y and b=3 into the formula to obtain the factored form.

Final Answer

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

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