# Math

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I have no clue how to do this as no values were given and im confused. can someone explain plz?

if x^3-y^3=m and x-y=N, express xy in terms of M and N

This is one of those pure manipulation problems.

you have to know that x^3-y^3 = (x-y)(x^2+xy+y^2)
so n(x^2+xy+y^2)=m
(x^2+xy+y^2) = m/n (#1)

notice we have xy, which is what we want, inside the bracket, but there is that x^2+y^2 hanging around

(from countless years of experience I know)
x^2+y^2 = (x-y)^2 + 2xy

so let's put that back in #1
((x-y)^2 + 2xy + xy) = m/n
n^2 + 3xy = m/n
3xy = m/n - n^2
3xy = (m-n^3)/n
and finally

xy = (m-n^3)/(3n)

I don't know what grade level you are in but that is pretty nasty.

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