Question

Which of the following must be true for an expression to be a difference of two squares?

a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients

A. a, b, and c
B. b and c
C. a and b
D. a and c

Answer 1

C.
An example of this is:
a² - b²
Where both terms have an even power and there are only two terms.

Answer 2

C is the correct option.

Explanation:

The true statements are :

a. all variables are raised to an even power

b. there are only two terms.

Here, we will take the example of:
`x^(2)-25`

This equation consists of two perfect squares,
`x^(2)` and
`5^(2)`. The variables are raised to even power (2) and also the equation has 2 terms.

Upon factoring we get
`(x+5)(x-5)`.

Therefore, we can say that the difference of two squares means that both terms of the equation should be square numbers. This is not possible for more than 2 terms.