Chapter 7.2, Problem 25E

To determine

To calculate: The product of the polynomial $(q-\frac{3}{4})(q+\frac{1}{4})$ using FOIL (Firsts Outsides Insides Lasts) method.

Answer to Problem 25E

The product of the polynomial $(q-\frac{3}{4})(q+\frac{1}{4})$ using FOIL method is $=q^2-\frac{2q}{4}-\frac{3}{16}$

Explanation of Solution

Given information:

The given polynomial is $(q-\frac{3}{4})(q+\frac{1}{4})$ , where ‘q’ is a variable

Calculation:

On multiplying first term of both binomials,

  $q\times q=q^2$

On multiplying outside terms of each binomial,

  $q\times \frac{1}{4}=\frac{q}{4}$

On multiplying inside terms of both binomials,

  $(-\frac{3}{4})\times q=-\frac{3}{4}q$

On multiplying last terms of each binomial,

  $(-\frac{3}{4})\times \frac{1}{4}=-\frac{3}{16}$

On adding all these terms,

  $(q-\frac{3}{4})(q+\frac{1}{4})$ $=q^2+\frac{q}{4}-\frac{3q}{4}-\frac{3}{16}$

  $=q^2-\frac{2q}{4}-\frac{3}{16}$

  $=q^2-\frac{q}{2}-\frac{3}{16}$

Thus, the required product of the given polynomial is $q^2-\frac{q}{2}-\frac{3}{16}$ .