Factor 9x^2-12x+4

Problem

9*x2−12*x+4

Solution

1. Identify the expression as a quadratic trinomial of the form a*x2+b*x+c where a=9 b=−12 and c=4

2. Recognize that the first term 9*x2 is a perfect square, (3*x)2 and the last term 4 is a perfect square, 2

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(3x)(2) = 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*m*a*t*c*h*e*s(t)*h*e*p*a*t*t*e*r*n3x - 2)^2$.

5. Write the factored form using the perfect square trinomial identity.

Final Answer

9*x2−12*x+4=(3*x−2)2

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