Question

Expand the polynomial. 1. (m^2-n)(m^2+2n^2)2. (a-2)(4a^3-3a^2)

Answer 1

1)

The given polynomial is

`(m^2-n)(m^2+2n^2)`

Multiply as follows:

`(m^2-n)(m^2+2n^2)=m^2(m^2+2n^2)-n(m^2+2n^2)`

`=m^2* m^2+m^2*2n^2-n* m^2-n*2n^2`

`=m^4+2m^2n^2-m^2n-2n^3`

Hence the required expansion is

`(m^2-n)(m^2+2n^2)=m^4+2m^2n^2-m^2n-2n^3`

2)

The given polynomial is

`(a-2)(4a^3-3a^2)`

Multiply as follows:

`(a-2)(4a^3-3a^2)=a(4a^3-3a^2)-2(4a^3-3a^2)`

`=a*4a^3-a*3a^2-2*4a^3-(-2)*3a^2`

`=4a^4-3a^3-8a^3+6a^2`

`=4a^4-11a^3+6a^2`

Hence the required expansion is

`(a-2)(4a^3-3a^2)=4a^4-11a^3+6a^2`