Factor 4x^2+28x+49

Problem

4*x^2+28*x+49

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=4 b=28 and c=49

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

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 a^2+2*a*b+b^2=(a+b)^2

Final Answer

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

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