Chapter 8.7, Problem 51HP

To determine

To describe the reason for no middle term in the difference of squares.

Explanation of Solution

When the difference of squares pattern is multiplied together using the FOIL method

(multiplying the first terms, outer terms, inner terms and last term), the outer and inner terms are opposites of each other.

When these terms are added together, the sum is zero.

Therefore, there can be no middle term in the difference of squares.

For Example,

  $\begin{array}{c}{x}^2-16=(x-4)(x+4)\\ =x^2-4x+4x-16\\ =x^2-16\end{array}$

Here, the middle term vanishes.