Factor 9x^2+42x+49

Problem

9*x^2+42*x+49

Solution

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

2. Determine the square root of the first term, 9*x^2 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, a^2+2*a*b+b^2=(a+b)^2 using a=3*x and b=7

Final Answer

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

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