Question

Multiply the following binomials by monomials

$\left(-\frac{4}{5}x\right)\times \left(\frac{3}{4}xy-\frac{4}{7}yz\right)$

Answer 1

Finding the multiplication

Multiplying by the horizontal method

$$\begin{gathered} \left(-\frac{4}{5}x\right)\times \left(\frac{3}{4}xy-\frac{4}{7}yz\right)=\left(-\frac{4}{5}x\right)\times \left(\frac{3}{4}xy\right)-\left(-\frac{4}{5}x\right)\times \left(\frac{4}{7}yz\right) \\ =\left(-\frac{4}{5}\times \frac{3}{4}\right)\left(x\times xy\right)-\left(-\frac{4}{5}\times \frac{4}{7}\right)\left(x\times yz\right) \\ =-\frac{3}{5}{x}^{2}y+\frac{16}{35}xyz \end{gathered}$$

Hence, the product of algebraic expression is $-\frac{3}{5}{x}^{2}y+\frac{16}{35}xyz$.