Question

Simplify: ${(3pq+3qr)}^2-18p{q}^{2}r$ (3 marks)

Answer 1

Given expression
${(3pq+3qr)}^2-18p{q}^{2}r$

In given expression,
${(3pq+3qr)}^{2}isinformof{(a+b)}^2$
(0.5 marks)
We know that
${(a+b)}^2=a^2+2ab+b^2$ (0.5 marks)

Similarly
${(3pq+3qr)}^2={\left(3pq\right)}^2+2\times 3pq\times 3qr+{\left(3qr\right)}^2=9p^2{q}^2+18p{q}^{2}r+9q^2{r}^2$
(1 mark)

Finally,
${(3pq+3qr)}^2-18p{q}^{2}r=9p^2{q}^2+18p{q}^{2}r+9q^2{r}^2-18p{q}^{2}r=9p^2{q}^2+9q^2{r}^2$
(1 mark)