Question

Find the quotient of each of the following

$\left(32x^{2}y-9y^2+6z{y}^2\right)÷3y$

Answer 1

Finding quotient

First, write the given expression in fractional form as:

$\left(32x^{2}y-9y^2+6z{y}^2\right)÷3y=\frac{32x^{2}y-9y^2+6z{y}^2}{3y}$

Divide the literal and numerical coefficients of each term of the numerator by denominator,

$$\begin{gathered} \frac{32x^{2}y-9y^2+6z{y}^2}{3y}=\frac{32x^{2}y}{3y}-\frac{9y^2}{3y}+\frac{6z{y}^2}{3y} \\ =\frac{32x^2}{3}-3y+2zy \end{gathered}$$

Hence, $\left(32x^{2}y-9y^2+6z{y}^2\right)÷3y==\frac{32x^2}{3}-3y+2zy$