we are given
[tex](5x^2 -3xy +10y^2) - (12x^2+11xz-7z^2)[/tex]
we have to subtract
step-1: Distribute negative sign
[tex]=5x^2 -3xy +10y^2-12x^2-11xz+7z^2[/tex]
step-2:Combine like terms
[tex]=5x^2 -12x^2-3xy -11xz+10y^2+7z^2[/tex]
[tex]=-7x^2-3xy -11xz+10y^2+7z^2[/tex]
we get
[tex]=-7x^2-3xy -11xz+10y^2+7z^2[/tex]............Answer