Given expression:
[tex](5x^2+7xy-y^2)-(4x^2-xy-2y)[/tex]To simplify the expression, we apply the rules of BODMAS.
First, we open the bracket. Recall that:
[tex]\begin{gathered} -\text{ }\times\text{ - = +} \\ -\text{ }\times\text{ + = -} \end{gathered}[/tex]When we open the bracket, we have:
[tex]=5x^2+7xy-y^2-4x^2+xy+2y^{}[/tex]Collect like terms:
[tex]\begin{gathered} =5x^2-4x^2-y^2+2y^{}\text{ + 7xy + xy} \\ =x^2-y^2+2y\text{ +8xy} \end{gathered}[/tex]Hence, the new expression is:
[tex]=x^2-y^2\text{ + 2y + 8xy}[/tex]