Factor 4x^2+28x+49

Problem

4*x2+28*x+49

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=4 b=28 and c=49

2. Recognize that the first term 4*x2 is a perfect square, (2*x)2 and the last term 49 is a perfect square, 7

3. Check if the middle term 28*x fits the pattern 2*a*b for a perfect square trinomial (a+b)2

4. Verify the calculation: 2(2x)(7) = 28x$, which matches the middle term.

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

Final Answer

4*x2+28*x+49=(2*x+7)2

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