Factor 16x^2+24x+9

Problem

16*x2+24*x+9

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=16 b=24 and c=9

2. Recognize that the first term 16*x2 is a perfect square, (4*x)2

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

4. Verify if the middle term 24*x matches the pattern 2*a*b for a perfect square trinomial (a+b)2

2*(4*x)*(3)=24*x

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

(4*x)2+2*(4*x)*(3)+3=(4*x+3)2

Final Answer

16*x2+24*x+9=(4*x+3)2

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