Chapter 4.3, Problem 1WE

To determine

To Find:

The product ..

Answer to Problem 1WE

  $\left(3v+1\right)\left(2v-5\right)=16v^2-13v-5$

Explanation of Solution

Given Information:

Given expression:

  $\left(3v+1\right)\left(2v-5\right)$

Concept Used :

FOIL method for multiplying the binomials:

• This is a method for multiplying two binomials.
• The letters of FOIL stand for First, Outer, Inner, Last.
• First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.Inner means multiply the innermost terms in the product and Last means multiply the terms which occur last in each binomial.
• Then add all the products to get the solution.

Calculation:

  $\left(3v+1\right)\left(2v-5\right)$

Use FOIL method:

F represents the multiplication of first terms of each binomial = $\text{3v}\cdot 2v=6v^2$

O represents the multiplication of the outermost terms of the product = $\text{ 3v}\cdot (-5)=-15v$

I represents the multiplication of the innermost terms of the product = $\text{1}\cdot 2v=2v$

L represents the multiplication of the last terms of each binomial = $\text{1}\cdot (-5)=-5$

Add all the products:

  $\begin{array}{l}\left(3v+1\right)\left(2v-5\right)\\ =16v^2-15v+2v-5\\ =16v^2-13v-\mathrm{5............}[combine\text{ like terms]}\\ \text{So,}\\ \left(3v+1\right)\left(2v-5\right)=16v^2-13v-5\end{array}$