Factor 36x^2-12x+1

Problem

36*x2−12*x+1

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=36 b=−12 and c=1

2. Recognize that the first term 36*x2 is a perfect square, (6*x)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 a2−2*a*b+b2 which factors into (a−b)2

4. Verify the middle term by calculating 2(6x)(1) = 12x.S*i*n*c*e*t*h*e*m*i*d(d(l))*e*t*e*r*m*i*s()12x,t*h*e*e*x*p*r*e*s(s(i))*o*n*ƒ*i*t*s(t)*h*e*p*a*t*t*e*r*n6x - 1)^2$.

5. Write the expression in its factored form.

Final Answer

36*x2−12*x+1=(6*x−1)2

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