Factor 9x^2+12x+4

Problem

9*x^2+12*x+4

Solution

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

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

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

4. Verify the middle term by calculating 2⋅(3*x)⋅2=12*x

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

6. Substitute a=3*x and b=2 into the formula to get (3*x+2)^2

Final Answer

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

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