Question

Subtract $5{\mathrm{a}}^2-7\mathrm{ab}+5{\mathrm{b}}^2$ from $3\mathrm{ab}-2{\mathrm{a}}^2-2{\mathrm{b}}^2$.

Answer 1

Subtract $5{\mathrm{a}}^2-7\mathrm{ab}+5{\mathrm{b}}^2$ from $3\mathrm{ab}-2{\mathrm{a}}^2-2{\mathrm{b}}^2$.

$$\begin{gathered} \left(3\mathrm{ab}-2{\mathrm{a}}^2-2{\mathrm{b}}^2\right)-\left(5{\mathrm{a}}^2-7\mathrm{ab}+5{\mathrm{b}}^2\right) \\ =3\mathrm{ab}-2{\mathrm{a}}^2-2{\mathrm{b}}^2-5{\mathrm{a}}^2+7\mathrm{ab}-5{\mathrm{b}}^2 \\ =-2{\mathrm{a}}^2-5{\mathrm{a}}^2-5{\mathrm{b}}^2-2{\mathrm{b}}^2+7\mathrm{ab}+3\mathrm{ab} \\ =-7{\mathrm{a}}^2-7{\mathrm{b}}^2+10\mathrm{ab} \end{gathered}$$

Therefore, the required answer is $-7{\mathrm{a}}^2-7{\mathrm{b}}^2+10\mathrm{ab}$.