Question

Which of the following is an example of the difference of two squares

Answer 1

Complete Question: Which of the following is an example of the difference of two​ squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. $x^2 - 9$.

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: $a^2 - b^2 = (a + b)(a - b)$.

a² and b² are perfect squares. Expanding $(a + b)(a - b)$ will give us $a^2 - b^2$.

Therefore, an example of the difference of two squares, from the given options, is $x^2 - 9$.

$x^2 - 9$ can be factorised as $x^2 - 3^2 = (x + 3)(x - 3)$.