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

The correct answers are:

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

Step-by-step 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.

Answer 2

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.