Factor y^2+8y+16

Problem

y^2+8*y+16

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y^2+b*y+c where a=1 b=8 and c=16

2. Recognize that the expression is a perfect square trinomial because the first term is y^2 the last term is 4^2 and the middle term is 2*(y)*(4)

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

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

Final Answer

y^2+8*y+16=(y+4)^2

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