Factor x^2-16x+64

Problem

x2−16*x+64

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x2+b*x+c where a=1 b=−16 and c=64

2. Recognize that the expression is a perfect square trinomial because the first term is x2 the last term is 8 and the middle term is −2*(x)*(8)

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

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

Final Answer

x2−16*x+64=(x−8)2

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