Chapter 14, Problem 27SGR

To determine

To calculate: The multiplication of the factored form of the polynomial $8x\left(2x^2+3x\right)$ .

Answer to Problem 27SGR

The multiplication of the polynomial expression $8x\left(2x^2+3x\right)$ is $16x^3+24x^2$ .

Explanation of Solution

Given Information:

The expression is $8x\left(2x^2+3x\right)$ .

Formula Used:

Distribution formula is:

  $\begin{array}{c}\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)\\ =a\times c+a\times d+b\times c+b\times d\end{array}$

Calculation:

The given expression is $8x\left(2x^2+3x\right)$ .

Now find the multiplication of the polynomial $8x\left(2x^2+3x\right)$ .

Use the formula $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)=a\times c+a\times d+b\times c+b\times d$

  $\begin{array}{c}8x\left(2x^2+3x\right)=\left(8x\right)\left(2x^2\right)+\left(8x\right)\left(3x\right)\\ =16x^3+24x^2\end{array}$

Hence, the requiredmultiplication of the polynomial expression $8x\left(2x^2+3x\right)$ is $16x^3+24x^2$ .