question_answer

Simplify:

(a)                                \[-\text{ }pcr\text{ }\left( {{p}^{2}}+{{q}^{2}}+{{r}^{2}} \right)\]

(b)                                                                       \[(px+qy)(ax-by)\]

Answer:

(a)                                             \[pqr({{p}^{2}}+{{q}^{2}}+{{r}^{2}})\]

\[=(pqr)\times {{p}^{2}}(pqr)\times {{q}^{2}}(pqr)\times {{r}^{2}}\]

\[=\text{ }{{p}^{3}}qrp{{q}^{3}}rpq{{r}^{3}}\]

(b)                                                  \[(px+qy)\text{ }(axby)\]

\[=px(axby)+qy(axby)\]

\[=ap{{x}^{2}}pbxy+aqxyqb{{y}^{2}}\].