Chapter 4.3, Problem 33WE

To determine

To calculate: The multiplication of the term $\left(a+2b\right)\left(a^3-2a^{2}b-b^3\right)$ .

Answer to Problem 33WE

The required multiplication is $a^4-a{b}^3-4a^2{b}^4-2b^4$ .

Explanation of Solution

Given information:

The algebraic term is $\left(a+2b\right)\left(a^3-2a^{2}b-b^3\right)$ .

Formula Used:

Distribution property is

  $\begin{array}{c}\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)\\ =ac+ad+bc+bd\end{array}$

Calculation:

Consider the given algebraic term $\left(a+2b\right)\left(a^3-2a^{2}b-b^3\right)$ .

Now multiply. Use the distribution property.

  $\begin{array}{c}\left(a+2b\right)\left(a^3-2a^{2}b-b^3\right)=a\left(a^3-2a^{2}b-b^3\right)+2b\left(a^3-2a^{2}b-b^3\right)\\ =a^4-2a^{3}b-a{b}^3+2a^{3}b-4a^2{b}^4-2b^4\\ =a^4-a{b}^3-4a^2{b}^4-2b^4\end{array}$

Hence, the required multiplication is $a^4-a{b}^3-4a^2{b}^4-2b^4$ .