Question

Is the sum of $2$ binomials always a binomial?

• A. True
• B. False

Answer 1

The correct option is B False

Determining why the sum of two binomials is not always a binomial:

The sum of two binomials can be a binomial only if the terms are to the same power for both terms within both binomials.

Example $1$:

Let's consider the equation

$$\begin{gathered} \left(x+y\right)+\left(x-y\right)=x+y+x-y \\ =2x \end{gathered}$$

Example $2$:

$$\begin{gathered} \left(x+y\right)+\left(-x-y\right)=x+y-x-y \\ =0 \end{gathered}$$

The above two examples prove that the sum of two binomials is not always a binomial.

Therefore, the given statement is false.