# How do I factor this problem `-105m^6n+28m^5n^2+21m^4n^3`

### 3 Answers | Add Yours

We have given

`-105m^6n+28m^5n^2+21m^4n^3`

`HCF (105,28,21)=7`

`HCF (m^6n,m^5n^2,m^4n^3)=m^4n`

`Thus` factor out `7m^4n` from the given expression

`-7m^4n(15m^2-4mn-3n^2)`

splitting the middle term ,in the bracket

`-7m^4n(15m^2-9mn+5mn-3n^2)`

`-7m^4n(3m(5m-3n)+n(5m-3n))`

`-7m^4n(5m-3n)((3m+n)`

which is required facors.

**Sources:**

`-105m^6n+28m^5n^2+21m^4n^3` `=7m^4n(-15m^2+4mn+3n^2)=` `-7m^4n(15m^2-4mn-3n^2)=` `-7m^4n(15m^2+5mn -9mn-3n^2)=`

`-7m^4n[5m(3m+n)-3n(3m+n)]=` `-7m^4n(5m-3n)(3m+n)`

No. the answer is -7m^4n(3m+n)(5m-3n)