# Binomials

## Related Calculator: Polynomial Calculator

**Binomial** is a sum/difference of TWO monomials.

Both monomials are called **terms**.

**Examples of binomials** are:

- `5+x`
- `2x^2+y^3x`
- `10xy^3-zy^2x`

**Examples of expressions, that are not binomials**:

- `x+1/x` (second term is not a monomial)
- `(2-y)/x` (division is not allowed)
- `xy^2+z-2` (binomial can have only TWO terms)

**Degree of the binomial** is the largest number among degrees of its monomials.

For example, in binomial `4x^2y^3-9z^8y^7` first term has degree `2+3=5` and second term has degree `8+7=15`. The largest of numbers 5 and 15 is 15. Thus, degree of the `4x^2y^3-9z^8y^7` is 15.

**Exercise 1**. Determine whether the following is a binomial: `2/5x-3/5y`?

**Answer**: yes.

**Exercise 2**. Determine whether the following is a binomial: `1/x+2y+3`?

**Answer**: no.

**Exercise 3**. Determine whether the following is a binomial: `sqrt(3)x*y+5zy`?

**Answer**: yes.

**Exercise 4**. Find degree of the following expression: `-xy+5`?

**Answer**: 2.

**Exercise 5**. Find degree of the following expression: `-p^3q^9+5z^3y^4p^(10)`?

**Answer**: 17.