Question

Multiply the quotients obtained by dividing $24(x^4{y}^3{z}^3+x^3{y}^3{z}^4+x^3{y}^4{z}^3)$ by $8x^3{y}^3{z}^3$ and $25xyz(6x^2+13x+5)$ by $5(3x+5)$.

• A. $3xyz(x+y+z)(2x+1)$
• B. $15xyz(x+y+z)(2x+1)$
• C. $5xyz(x+y+z)(2x+1)$
• D. $15\left(xyz{)}^2\right(x+y+z\left)\right(2x+1)$

Answer 1

The correct option is B

$15xyz(x+y+z)(2x+1)$

$\frac{24(x^4{y}^3{z}^3+x^3{y}^3{z}^4+x^3{y}^4{z}^3)}{8x^3{y}^3{z}^3}$
$=\frac{24\left(x^3{y}^3{z}^3\right)(x+y+z)}{8x^3{y}^3{z}^3}$
$=3(x+y+z)$


$\frac{25xyz\left(3x\right(2x+1)+5(2x+1)}{5(3x+5)}$
$=\frac{25xyz\left(\right(3x+5\left)\right(2x+1)}{5(3x+5)}$
$=5xyz(2x+1)$

Product of quotients $=3(x+y+z)\times 5xyz(2x+1)$
$=15xyz(x+y+z)(2x+1)$