Factor y^2+16y+64

Problem

y2+16*y+64

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y2+b*y+c where a=1 b=16 and c=64

2. Recognize that the expression is a perfect square trinomial because the first term is y2 the last term is 8 and the middle term is 2⋅y⋅8

3. Apply the formula for a perfect square trinomial, which states a2+2*a*b+b2=(a+b)2

4. Substitute a=y and b=8 into the formula to obtain the factored form.

Final Answer

y2+16*y+64=(y+8)2

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