Factor 9x^2-48x+64

Problem

9*x^2−48*x+64

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c and check if the first and last terms are perfect squares.

2. Recognize that 9*x^2 is (3*x)^2 and 64 is 8^2

3. Verify if the middle term fits the pattern for a perfect square trinomial, which is −2*a*b

4. Calculate the middle term using a=3*x and b=8

−2*(3*x)*(8)=−48*x

5. Apply the formula for a perfect square trinomial (a−b)^2=a^2−2*a*b+b^2

6. Substitute the values into the formula to get (3*x−8)^2

Final Answer

9*x^2−48*x+64=(3*x−8)^2

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