Question

Divide: 81(p⁴q²r³ + 2p³q³r² – 5p²q²r²) by (3pqr)²

Answer 1

${\displaystyle \frac{81({\text{p}}^4{\text{q}}^2{\text{r}}^3+2{\text{p}}^3{\text{q}}^3{\text{r}}^2-5{\text{p}}^2{\text{q}}^2{\text{r}}^2)}{{\left(3\text{pqr}\right)}^2}}$

= ${\displaystyle \frac{81\left({\text{p}}^2{\text{q}}^2{\text{r}}^2\right)({\text{p}}^2\text{r}+2\text{pq}-5)}{9\left({\text{p}}^2{\text{q}}^2{\text{r}}^2\right)}}$

= ${\displaystyle \frac{81}{9}{\left({\text{p}}^2{\text{q}}^2{\text{r}}^2\right)}^{1-1}({\text{p}}^2\text{r}+2\text{pq}-5)}$ 

= 9(p²r + 2pq – 5)

= 9p²r + 18pq – 45