Question

Determine whether the binomial can be written as a difference of two squares.

Answer 1

Technically, all of the choices can be written as a difference of squares. Just find the square root of both terms and use the formula

$a^2 - b^2 = (a + b)(a - b)$

where $a$ and $b$ are terms.

However, I am going to assume that your problems want to know if the expressions can be written as a difference of two squares, where $a^2$ and $b^2$ are either variables with an even exponent or a perfect square, as this is what many instructors are asking for.

A) A cannot be written as a difference of two squares, because even though 25 is a square, $p^9$ is not a variable with an even exponent, which means that we can not apply the Differences of Squares.

B) Similar to Choice A, we cannot apply the Differences of Squares given the context because 18 is not a perfect square.

C) We can apply it to Choice C, since $g$ has an even exponent and 36 is a perfect square. Applying the formula, we get:

$g^2 - 36 = (g + 6)(g - 6)$