Uniting literal coefficients using parentheses?
I don't understand why the subtrahend coefficients changed places in the answer. Here are the two subtraction problems:
ax - by
2x - cy
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(a - 2)x + (c - b)y
mx - ny
nx - my
-----------
(m - n)x + (m - n)y
I do understand how to work the problems and the rule for subtraction as to changing the sign of the subtrahend and adding. I cannot find the reason or answer WHY the second column of coefficients *change their order* in the answers, i.e., (- b - c) to +(c - b), and (- n - m) to +(m - n). Is it because the latter coefficients (c and m) are to be next to their changed sign, i.e., the positive one? Does it really matter what order the subtrahends are in? The text does not explain.
Thank you.
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Verified answer
If you just work it out, the first one becomes (a - 2)x + (-b - (-c))y. This second term can be rewritten as: (a - 2)x + (-b + c)y. This usually gets rewritten to (c - b) because that's easier to read. The order does not matter, so we might as well take the order that is easiest to read.
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