Factor 9x^2+42x+49

Problem

9*x2+42*x+49

Solution

1. Identify the structure of the expression as a potential perfect square trinomial of the form a2+2*a*b+b2

2. Determine the square root of the first term, 9*x2 which is 3*x

3. Determine the square root of the last term, 49 which is 7

4. Verify the middle term by calculating 2*a*b which is 2(3x)(7) = 42x$.

5. Apply the formula for a perfect square trinomial, a2+2*a*b+b2=(a+b)2 using a=3*x and b=7

Final Answer

9*x2+42*x+49=(3*x+7)2

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