Question

Divide:
(i) 24x²y³ by 3xy
(ii) 36xyz² by −9xz
(iii) −72x²y²z by −12xyz
(iv) −56mnp² by 7mnp

Answer 1

(i) 24x²y³ by 3xy

$$\begin{gathered} \frac{24x^2{y}^3}{3xy} \\ \Rightarrow \left({\displaystyle \frac{24}{3}}\right)\left(x^{2-1}\right)\left(y^{3-1}\right) \\ \Rightarrow 8x{y}^2. \end{gathered}$$

Therefore, the quotient is 8xy².

(ii) 36xyz² by −9xz

$$\begin{gathered} \frac{36xy{z}^2}{-9xz} \\ \Rightarrow \left({\displaystyle \frac{36}{-9}}\right)\left(x^{1-1}\right)\left(y^{1-0}\right)\left(z^{2-1}\right) \\ \Rightarrow -4yz \end{gathered}$$

Therefore, the quotient is −4yz.

(iii)
$$\begin{gathered} -72x^2{y}^{2}zby-12xyz \\ \frac{-72x^2{y}^{2}z}{-12xyz} \\ \Rightarrow \left(\frac{-72}{-12}\right)\left(x^{2-1}\right)\left(y^{2-1}\right)\left(z^{1-1}\right) \\ \Rightarrow 6xy \end{gathered}$$

Therefore, the quotient is 6xy.

(iv) −56mnp² by 7mnp


$$\begin{gathered} \frac{-56mn{p}^2}{7mnp} \\ \Rightarrow \left(\frac{-56}{7}\right)\left(m^{1-1}\right)\left(n^{1-1}\right)\left(p^{2-1}\right) \\ \Rightarrow -8p \end{gathered}$$

Therefore, the quotient is −8p.