Factor 16x^2-24x+9

Problem

16*x^2−24*x+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c

2. Recognize that the first term 16*x^2 is a perfect square, (4*x)^2

3. Recognize that the last term 9 is a perfect square, 3^2

4. Check if the middle term −24*x matches the pattern for a perfect square trinomial, −2*(4*x)*(3)

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

6. Substitute a=4*x and b=3 into the formula.

Final Answer

16*x^2−24*x+9=(4*x−3)^2

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