Q. 183 - Intermediate Algebra

Question

In the following exercises, multiply. 

$$\begin{gathered} \left(a\right) -5t\left(t^2+3t-18\right) \\ \left(b\right) 9r^{3}s\left(r^2-3rs+5s^2\right) \end{gathered}$$

Step-by-Step Solution

Answer

The solution is 

Step 1. Apply the concept of Distributive Property

If $A,B,C$ are any real numbers or algebraic expressions then,

$A\left(B+C\right)=\left(B+C\right)A=AB+AC$

Part (a) Step 1. Given information

The given expression is 

$-5t\left(t^2+3t-18\right)$

Part (a) Step 2. Simplify

Using Distributive property,

$$\begin{gathered} -5t\left(t^2+3t-18\right) \\ =\left(-5t\right)·t^2-5t·3t+5t·18 \\ =-5t^3-15t^2+90t \end{gathered}$$

Part (b) Step 1. Given expression

The given expression is 

$9r^{3}s\left(r^2-3rs+5s^2\right)$

Part (b) Step 2. Simplify

Using Distributive property

$$\begin{gathered} 9r^{3}s\left(r^2-3rs+5s^2\right) \\ =9r^{3}s·r^2-9r^{3}s·3rs+9r^{3}s·5s^2 \\ =9r^{5}s-27r^4{s}^2+45r^3{s}^3 \end{gathered}$$