Chapter 8.7, Problem 8LC

To determine

To find: If a binomial is a difference of two squares.

Answer to Problem 8LC

If both terms of the binomial are perfect squares, then their difference is a difference of two squares.

Explanation of Solution

Given information: Any binomial.

Concept used: A binomial is an expression with two terms in it and having negative sign between them.

Calculation: If two terms are not perfect squares, then take their greatest common factor out of both terms, so that both terms of binomial are now the difference of two perfect squares. For example,

  $\begin{array}{l}24x^2-6=6(x^2-1)\text{Take 6 out of both terms}\\ \text{=}6(x^2-1^2)\end{array}$

Conclusion: So, if both terms of the binomial are perfect squares, then it is difference of two squares.