Asked by Jerry
Factor completely
112r^2+392rp+343p^2
Please help
112r^2+392rp+343p^2
Please help
Answers
Answered by
DQR
All three numbers are quite large, so first of all try to find a common factor so you can make the problem smaller. Actually 7 will divide all three of them - so you can reduce it to:
7 x (16r^2 + 56rp + 49p^2)
Is the contents of that bracket the square of anything? There are no constants in the squared expression, so if it IS the square of anything, it would have to be (ar + bp) for some a and b. Now, 16 is the square of 4, and 49 is the square of 7, so let's consider (4r + 7p). That certainly gives us the r^2 and p^2 coefficients, and by a lucky coincidence, 2 x 7 x 4 = 56. So we've done it! (If that hadn't worked, we'd have looked at a = -7 and/or b = -7, which also might have worked, but in the event that wasn't necessary.)
7 x (16r^2 + 56rp + 49p^2)
Is the contents of that bracket the square of anything? There are no constants in the squared expression, so if it IS the square of anything, it would have to be (ar + bp) for some a and b. Now, 16 is the square of 4, and 49 is the square of 7, so let's consider (4r + 7p). That certainly gives us the r^2 and p^2 coefficients, and by a lucky coincidence, 2 x 7 x 4 = 56. So we've done it! (If that hadn't worked, we'd have looked at a = -7 and/or b = -7, which also might have worked, but in the event that wasn't necessary.)
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