Question

Multiply the following binomials by monomials

$\left(a{x}^2\right)\times (-b{y}^2-c^{2}x)$

Answer 1

Finding the multiplication

Multiplying by the horizontal method

$$\begin{gathered} \left(a{x}^2\right)\times (-b{y}^2-c^{2}x)=\left(a{x}^2\right)\times \left(-b{y}^2\right)-\left(a{x}^2\right)\times \left(c^{2}x\right) \\ =\left(1\times \left(-1\right)\right)\left(a{x}^2\times b{y}^2\right)-\left(1\times 1\right)\left(a{x}^2\times c^{2}x\right) \\ =-ab{x}^2{y}^2-a{c}^2{x}^3 \end{gathered}$$

Hence, the product of algebraic expression is $-ab{x}^2{y}^2-a{c}^2{x}^3$.