Question

(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree?

$\left(5x+2y\right)\left(5x-2y\right)$

Short answer

The given polynomial is a binomial of degree 2.

Step-by-step solution

Step 1. Given Information

The given polynomial is$\left(5x+2y\right)\left(5x-2y\right)$.

Part (a) Step 1. Count the Terms in Simplified Polynomial  

• Simplify the given expression as follows:

$$\begin{gathered} \left(5x+2y\right)\left(5x-2y\right)={\left(5x\right)}^2-{\left(2y\right)}^2 \\ =25x^2-4y^2 \end{gathered}$$

• As the polynomial has 2 terms, it is a binomial.

Part (b) Step 1. Find the Highest Power 

• Both the terms in the simplified expression have the power 2.
• SO, the degree of the binomial is 2.