Question

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

• A. $9p^2$$q^2$ + $9q^2$$r^2$ - $18p{q}^2$r
• B. $9p^2$$q^2$ + $9q^2$$r^2$ - $9p{q}^2$r
• C. $9p^2$$q^2$ + $9q^2$$r^2$
• D. $9p^2$$q^2$ + $9q^2$$r^2$ + $9p{q}^2$r

Answer 1

The correct option is C

$9p^2$$q^2$ + $9q^2$$r^2$

${(3pq+3qr)}^2$
Expand this using the identity
${(a+b)}^2=a^2+2ab+b^2$

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

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