Question

(m-n)^2-(2m+3n)^2
Factor - the answer is -(m+4n)(3m+2n)
Don't know how to get there?

Answer 1

well look at it this way

(m - n)^2 = m^2 - 2mn + n^2
- (2m+3n)^2 = 4m^2 + 12mn + 9n^2 do the subtraction
-------------------
-3m^2 -14mn - 8n^2

factor out the negative -(3m^2 + 14mn + 8m^2)

now factor there quadratic... start with 3m^2 3 is prime so use 3m and m
all terms are positive so then

so it becomes -(3m + ?? n)(m + ? n)

so you just need the factors of 8 so the middle term becomes 14mn