Chapter 4.3, Problem 30WE

To determine

To calculate: The multiplication of the term $\left(3-k^2\right)\left(2-k^2-k^4\right)$ .

Answer to Problem 30WE

The required multiplication is $6-5k^2-4k^4-k^6$ .

Explanation of Solution

Given information:

The algebraic term is $\left(3-k^2\right)\left(2-k^2-k^4\right)$ .

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 $\left(3-k^2\right)\left(2-k^2-k^4\right)$ .

Now multiply. Use the distribution property.

  $\begin{array}{c}\left(3-k^2\right)\left(2-k^2-k^4\right)=3\left(2-k^2-k^4\right)-k^2\left(2-k^2-k^4\right)\\ =6-3k^2-3k^4-2k^2-k^4-k^6\\ =6-5k^2-4k^4-k^6\end{array}$

Hence, the required multiplication is $6-5k^2-4k^4-k^6$ .