Chapter 4.3, Problem 22WE

To determine

To multiply given expression assuming exponents representing positive integers

Answer to Problem 22WE

  $x^4-9x^2$

Explanation of Solution

Given information : 

Given expression $x^2\left(x-3\right)\left(x+3\right)$

Concept used:

Using identity

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

And

Basic rule of multiplication of monomial and binomial

  $x\left(a+b\right)=\left(x\times a\right)+\left(x\times b\right)$

Rule of exponents

  $a^m.a^n=a^{m+n}$

Explanation: 

  $\begin{array}{l}{x}^2\left(x-3\right)\left(x+3\right)\\ =x^2\left({\left(x\right)}^2-{\left(3\right)}^2\right)\\ =x^2\left(x^2-9\right)\\ =\left(x^2\times x^2\right)-\left(9\times x^2\right)\\ =\left(x^{2+2}\right)-9x^2\\ =x^4-9x^2\end{array}$