Factor 16x^2-8x+1

Problem

16*x^2−8*x+1

Solution

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

2. Recognize that the expression is a perfect square trinomial because the first term 16*x^2 is (4*x)^2 the last term 1 is 1^2 and the middle term −8*x is 2*(4*x)*(−1)

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

4. Substitute a=4*x and b=1 into the formula to obtain the factored form.

Final Answer

16*x^2−8*x+1=(4*x−1)^2

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