Chapter 4.6, Problem 26WE

To determine

To multiply: the expression $\left(2n-5\right)\left(2n^2-3n-2\right)$ using horizontal form.

Answer to Problem 26WE

The result of multiplication is $4n^3-16n^2+11n+10$ .

Explanation of Solution

Given:

The expression is $\left(2n-5\right)\left(2n^2-3n-2\right)$ .

Calculation:

Steps in horizontal form method are:

• Separate the two binomials using multiplication sign.
• Multiply first binomial with each terms of second.
• Combine of add the like terms.

The given expression is solved as follows:

  $\begin{array}{l}\Rightarrow \left(2n-5\right)\left(2n^2-3n-2\right)\\ \Rightarrow \left(2n\right)\times \left(2n^2-3n-2\right)-5\times \left(2n^2-3n-2\right)\\ \Rightarrow 4n^3-6n^2-4n-10n^2+15n+10\\ \Rightarrow 4n^3-16n^2+11n+10\end{array}$

Thus, the result of multiplication is $4n^3-16n^2+11n+10$ .