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4m • mn • n - 49x • xn • np • p

label Algebra
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Jul 19th, 2014

What did your book say you should do with the equation? I will assume that you are supposed to simplify (reduce) it. We can do this by collecting terms. Since some of the terms above (terms refers to "4m" and "49x"  for instance) are multiplied, we can group them any way we like because multiplication is commutative (order in the equation doesn't matter). Let's start with the variable m. There are only two places you see it, the first term and also the second term. If we group them we get a 4, an m, another m, and an n. So, the grouping of the first and second term is 4m^2n (four times m squared times n). Now we put that in to replace the first two terms:

(4m^2n * n) - (49x * xn *np * p)

Let's keep grouping terms. You cannot group terms on either side of the minus sign until you have reduced the multplied terms. This is because subtraction is different from multiplication and multipliers have to be simplified separately from addition/subtraction terms. I have put parentheses above to highlight this. 

4m^2 * n = 4m^2*n^2                     49x * xn = 49x^2n                   49x^2n * np = 49x^2n^2p

49x^2n^2p * p = 49x^2n^2p^2

And now finally we put the substitutions together:

4m^2n^2 - 49x^2n^2p^2

This is the simplified answer and cannot be simplified further. Please check that this was the type of answer you need since the problem statement above needs more informatoin. 

Jul 20th, 2014

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