Question
Perform the following divisions: $\left(3 p q r-6 p^2 q^2 r^2\right) \div 3 p q$
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Answer
$\left(3 p q r-6 p^2 q^2 r^2\right) \div 3 p q$
$\frac{3\text{pqr}-6\text{p}^2\text{q}^2\text{r}^2}{3\text{pqr}}$
$=\frac{3\text{pqr}}{3\text{pq}}-\frac{6\text{p}^2\text{q}^2\text{r}^2}{3\text{pq}}$
$=\text{r}-\frac{2\times3\times\text{p}\times\text{p}\times\text{q}\times\text{q}\times\text{r}\times\text{r}}{3\times\text{p}\times\text{q}}$
$=\text{r}-2\text{pqr}^2$
$\frac{3\text{pqr}-6\text{p}^2\text{q}^2\text{r}^2}{3\text{pqr}}$
$=\frac{3\text{pqr}}{3\text{pq}}-\frac{6\text{p}^2\text{q}^2\text{r}^2}{3\text{pq}}$
$=\text{r}-\frac{2\times3\times\text{p}\times\text{p}\times\text{q}\times\text{q}\times\text{r}\times\text{r}}{3\times\text{p}\times\text{q}}$
$=\text{r}-2\text{pqr}^2$
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