1)
The given polynomial is
[tex](m^2-n)(m^2+2n^2)[/tex]Multiply as follows:
[tex](m^2-n)(m^2+2n^2)=m^2(m^2+2n^2)-n(m^2+2n^2)[/tex][tex]=m^2\times m^2+m^2\times2n^2-n\times m^2-n\times2n^2[/tex][tex]=m^4+2m^2n^2-m^2n-2n^3[/tex]Hence the required expansion is
[tex](m^2-n)(m^2+2n^2)=m^4+2m^2n^2-m^2n-2n^3[/tex]2)
The given polynomial is
[tex](a-2)(4a^3-3a^2)[/tex]Multiply as follows:
[tex](a-2)(4a^3-3a^2)=a(4a^3-3a^2)-2(4a^3-3a^2)[/tex][tex]=a\times4a^3-a\times3a^2-2\times4a^3-(-2)\times3a^2[/tex][tex]=4a^4-3a^3-8a^3+6a^2[/tex][tex]=4a^4-11a^3+6a^2[/tex]Hence the required expansion is
[tex](a-2)(4a^3-3a^2)=4a^4-11a^3+6a^2[/tex]