Chapter 8.3, Problem 5LC

To determine

To explain: The how to use FOIL method to find the product of two binomials.

Explanation of Solution

Given information:

The FOIL method is used to find the product of two binomials.

Formulaused:

FOIL stands for − First, Outer, Inner, Last that is used to find the product of two binomials.

Let we multiply two binomials $\left(px+q\right)$ and $\left(rx+s\right)$ by writing them in order $\left(px+q\right)\cdot \left(rx+s\right)$ .

Then the steps of multiplications they are:

Step1:

Multiply First terms of both binomials that is $px\cdot rx=\underset{\_}{pr{x}^2}$

Step2:

Multiply First terms of first binomials with outer of second term binomial that is $px\cdot s=\underset{\_}{psx}$

Step3:

Multiply second terms of first binomials with first term of second binomial that is $q\cdot rx=\underset{\_}{qrx}$

Step4:

Multiply second terms of first binomials with last term of second binomial that is $q\cdot s=qs$

(Note: Every term must be multiply carrying its sign)

Then finally add all products of four steps as, $\underset{\_}{pr{x}^2}+\underset{\_}{psx}+\underset{\_}{qrx}+qs$ .

Thus the product of binomials $\left(px+q\right)$ and $\left(rx+s\right)$ is $\underset{\_}{pr{x}^2}+\underset{\_}{psx}+\underset{\_}{qrx}+qs$ .

The diagram of FOIL method is shown in Figure-1 here.

  $\left(px+q\right)\left(rx+s\right)=\underset{\_}{pr{x}^2}+\underset{\_}{psx}+\underset{\_}{qrx}+qs=\underset{\_}{pr{x}^2}+\left(\underset{\_}{ps}+\underset{\_}{qr}\right)x+qs$