Factor y^2-16y+64

Problem

y^2−16*y+64

Solution

1. Identify the structure of the trinomial, which follows the form a*y^2+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 y^2 is (y)^2 the last term 64 is (8)^2 and the middle term −16*y is 2⋅y⋅(−8)

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=8 into the formula to obtain the factored form.

Final Answer

y^2−16*y+64=(y−8)^2

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