Question 298322: I need your help with an order of operations problem. First, I would like to state that I tried to work the problem, but was unable to come up with an answer. I know that the order of operations follows this list; parentheses(1), exponents(2), multiplication(3), division(4), addition(5), and subtraction(6). Using this knowledge has helped me break the problem down somewhat, but not completely.
Here is the problem as stated:  What number replaces the question mark? (The y represents the question mark. I was not able to punch the question mark in instead of the y because of a syntax error.)
I can deduce that the problems in the parentheses must be evaluated first, however, I'm not quite sure how to go about this. By combining like terms, I can see that 18x would combine with 3x, and 216 would combine with 36. However, they problems do not provide me with a classic distributive property solution.
Would you be able to enlighten me as far as what I can do when another situation such as this presents itself? Thanks!
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! solve 27x^3+216=(3x+y)(9x^2-18x+36) for y
factor
27*(x^3+8)=27*(x+2)*(x^2-2 x+4)
(9x^2-18x+36) =9*(x^-2x+4)
27*(x+2)*(x^2-2x+4) = 9*(x^2-2x+4)*(3x+y)
27/9=3
which you can see can be reduced to
3(x+2)=3x+y
3x+6=3x+y
6=y
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