Question

Subtract $4\mathrm{pq}-5{\mathrm{q}}^2-3{\mathrm{p}}^2$ from $5{\mathrm{p}}^2+3{\mathrm{q}}^2-\mathrm{pq}$.

Answer 1

We have to subtract $4\mathrm{pq}-5{\mathrm{q}}^2-3{\mathrm{p}}^2$ from $5{\mathrm{p}}^2+3{\mathrm{q}}^2-\mathrm{pq}$.

$$\begin{gathered} \left(5{\mathrm{p}}^2+3{\mathrm{q}}^2-\mathrm{pq}\right)-\left(4\mathrm{pq}-5{\mathrm{q}}^2-3{\mathrm{p}}^2\right) \\ =5{\mathrm{p}}^2+3{\mathrm{q}}^2-\mathrm{pq}-4\mathrm{pq}+5{\mathrm{q}}^2+3{\mathrm{p}}^2 \\ =5{\mathrm{p}}^2+3{\mathrm{p}}^2+3{\mathrm{q}}^2+5{\mathrm{q}}^2-\mathrm{pq}-4\mathrm{pq} \\ =8{\mathrm{p}}^2+8{\mathrm{q}}^2-5\mathrm{pq} \end{gathered}$$

Therefore, the required answer is $8{\mathrm{p}}^2+8{\mathrm{q}}^2-5\mathrm{pq}$.