Factor 4x^2+12x+9

Problem

4*x^2+12*x+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c where a=4 b=12 and c=9

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

3. Check if the middle term 12*x fits the pattern 2*a*b for a perfect square trinomial (a+b)^2

4. Verify the calculation: 2⋅(2*x)⋅3=12*x Since this matches the middle term, the expression is a perfect square trinomial.

5. Apply the formula for a perfect square trinomial a^2+2*a*b+b^2=(a+b)^2 using a=2*x and b=3

Final Answer

4*x^2+12*x+9=(2*x+3)^2

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