Factor 4x^2-12x+9

Problem

4*x2−12*x+9

Solution

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

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

3. Check if the middle term matches the pattern for a perfect square trinomial a2−2*a*b+b2 which requires the middle term to be −2*(2*x)*(3)

4. Verify the calculation: −2*(2*x)*(3)=−12*x which matches the middle term of the given expression.

5. Apply the formula for a perfect square trinomial a2−2*a*b+b2=(a−b)2

Final Answer

4*x2−12*x+9=(2*x−3)2

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