Chapter 8.7, Problem 55PFA

To determine

To find the true statement

Answer to Problem 55PFA

  $(x^4-9)$ is not a difference of squares

Explanation of Solution

Given:

Expression: $6x^5-54x$

Calculation:

Consider the given expression,

  $\Rightarrow 6x^5-54x$

Finding out the common term and taking it out,

  $\Rightarrow 6x(x^4-9)$

Further the above expression can be factored by difference of squares.

  $\Rightarrow (x^4-9)=((x^2)-3^2)=(x^2-3)(x^2+3)$

Thus, the completely factored form,

  $6x^5-54x=6x(x^2-3)(x^2+3)$

Conclusion:

Therefore, the statement which is true is: $(x^4-9)$ is not a difference of squares.