Question

Factorize:
$-12p{q}^{2}r+8p{r}^2+28p{q}^{2}r$

• A. $4pq(2p^2+r)$
• B. $8pr(15q^2+r)$
• C. $8pr(2q^2+r)$
• D. $4qr(2q^2+p)$

Answer 1

The correct option is C

$8pr(2q^2+r)$

$-12p{q}^{2}r+8p{r}^2+28p{q}^{2}r$
$=-12p{q}^{2}r+28p{q}^{2}r+8p{r}^2$
$=(-12+28)p{q}^{2}r+8p{r}^2$
$=16p{q}^{2}r+8p{r}^2$
$16p{q}^{2}r=2\times 8\times p\times q\times q\times r$
$8p{r}^2=2\times 4\times p\times r\times r$
$16p{q}^{2}r+8p{r}^2=2\times 2\times 2\times 2\times p\times q\times q\times r+2\times 2\times 2\times p\times r\times r$
$=8pr(2q^2+r)$