Question

Which of the following must be true for and expression to be a difference of two squares?
a. both coefficients are perfect squares.
b. there are only two terms.
c. both terms have negative coefficients.

Answer 1

Let's say e=a^2−b^2 and take each affirmation:

a. both coefficients are perfect squares.
a could be equal to 2 which is not a perfect square 

b. there are only two terms - obviously yes

c. both terms have negative coefficients - as we can see just b has a negative coefficient

Final answer b. there are only two terms.

Answer 2

The correct answers are:

a. both coefficients are perfect squares.; and b. there are only two terms.

Explanation:

In order to have a difference of squares, we will have only two terms.  Algebraically, this can be represented by a²-b².  This is by definition.

Since this is the difference of squares, both terms must be perfect squares.  If they are not, then it is no longer the difference of squares.