Factor 4x^2-4x+1

Problem

4*x^2−4*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=4 b=−4 and c=1

2. Recognize that the expression is a perfect square trinomial because the first term 4*x^2 is (2*x)^2 the last term 1 is (1)^2 and the middle term −4*x is −2*(2*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=2*x and b=1 into the formula to obtain the factored form.

Final Answer

4*x^2−4*x+1=(2*x−1)^2

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