Factor 4a^2-4a+1

Problem

4*a2−4*a+1

Solution

1. Identify the structure of the quadratic expression, which is in the form A*x2+B*x+C

2. Recognize that the first term 4*a2 is a perfect square, (2*a)2 and the last term 1 is also a perfect square, 1

3. Check if the middle term matches the pattern for a perfect square trinomial, x2−2*x*y+y2=(x−y)2

4. Verify the middle term by calculating 2(2a)(1) = 4a,w*h*i*c*h*m*a*t*c*h*e*s(t)*h*e*g*i*v*e*n*m*i*d(d(l))*e*t*e*r*m4a$ when using the subtraction sign.

5. Apply the formula for a perfect square trinomial to write the factored form.

Final Answer

4*a2−4*a+1=(2*a−1)2

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