Question

Multiply the following :

$\left(\frac{3}{5}m\right)\times \left(m{n}^2-\frac{3}{4}{l}^{2}m-2n^2+\frac{4}{7}lm{n}^2\right)$

Answer 1

Finding the multiplication

Multiplying by the horizontal method

$$\begin{gathered} \left(\frac{3}{5}m\right)\times \left(m{n}^2-\frac{3}{4}{l}^{2}m-2n^2+\frac{4}{7}lm{n}^2\right)=\frac{3}{5}m\times m{n}^2+\frac{3}{5}m\times \left(-\frac{3}{4}{l}^{2}m\right)+\frac{3}{5}m\times \left(-2n^2\right)+\frac{3}{5}m\times \frac{4}{7}lm{n}^2 \\ =\frac{3}{5}{m}^2{n}^2-\frac{9}{20}{m}^2{l}^2-\frac{6}{5}m{n}^2+\frac{12}{35}l{m}^2{n}^2 \end{gathered}$$

Hence, the product of a given algebraic expression is $\frac{3}{5}{m}^2{n}^2-\frac{9}{20}{m}^2{l}^2-\frac{6}{5}m{n}^2+\frac{12}{35}l{m}^2{n}^2$.