Chapter 4.4, Problem 1E

To determine

To complete: the given sentence.

Answer to Problem 1E

The expression $9x^4-49$ is in quadratic form because it can be written as $u^2-49$ where $u=3x^2$

Explanation of Solution

Given information:

Given sentence

“The expression $9x^4-49$ is in -------------form because it can be written as $u^2-49$ where $u=-------$ ”.

Calculation:

An expression of the form $a{u}^2+bu+c$ , here $u$ is an algebraic expression, is said to be in quadratic form.

Rewrite the expression $9x^4-49$ as

  $\begin{array}{c}9x^4-49={\left(3x\right)}^2-49\\ =u^2-49\left[\text{Let}u=3x^2\right]\end{array}$

Therefore, fill the blank space as “The expression $9x^4-49$ is in quadratic form because it can be written as $u^2-49$ Where $u=3x^2$ ”.