Factor 64x^2-16x+1

Problem

64*x2−16*x+1

Solution

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

2. Recognize that the first term 64*x2 is a perfect square, (8*x)2 and the last term 1 is also a perfect square, 1

3. Check if the middle term fits the pattern for a perfect square trinomial a2−2*a*b+b2=(a−b)2

4. Verify the middle term by calculating 2(8x)(1) = 16x,w*h*i*c*h*m*a*t*c*h*e*s(t)*h*e*m*a*g*n*i*t*u*d(e)*o*ƒ*t*h*e*g*i*v*e*n*m*i*d(d(l))*e*t*e*r*m16x$.

5. Apply the formula for a perfect square trinomial (a−b)2 using a=8*x and b=1

Final Answer

64*x2−16*x+1=(8*x−1)2

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