5 - 2m/mn + 7m + 4n + 28 times n + 7/8m^3 - 125. multiple rational expression

Question

I was able to figure out that 8m^3 - 125 could be (2m-5)(2m-5)(2m+5)

so would you do n(n + 4) + 7(m + 4)??

Thank you Rod!!!!!

Answer 1

I interpret this as (5-2m)/(mn+7m+4n+28) * (n+7)/(8m^3-125).

mn+7m+4n+28=mn+4n+7m+28=n(m+4)+7(m+4)=(n+7)(m+4).

8m^3-125: A^3-B^3=(A-B)(A^2+AB+B^2) so, putting A=2m and B=5, 8m^3-125=(2m-5)(4m^2+10m+25).

The original expression is (5-2m)/((n+7)(m+4)) * (n+7)/((2m-5)(4m^2+10m+25)).

The factor n+7 cancels out and so does 2m-5=-(5-2m).

So we get: -1/((m+4)(4m^2+10m+25))=-1/(4m^3+26m^2+65m+100).