The definition of a binomial is a reduced expression of two terms.
| Examples | Explanation of example |
| x + 3 | This expression has two terms, 'x' and '3' that are not like. |
| x2 + 5 | This expression has two terms, 'x2' and '3' that are not like. |
| x2 + x | This expression has two terms, 'x2' and x' that are not like. |
| x + 3 +2 | This expression actually can be simplified to x + 5 which is an expression that has two unlike terms. |
| x + x + 3 | This can be rewritten as 2x +3 which is an expression with two unlike terms. |
On the other hand, x+2x is not a binomial because x and 2x are like terms and can be reduced to 3x which is only one term. Remember, a binomial needs to be two separate terms that cannot be combined further.
| Examples | Explanation of example |
| 3 + 2 | This expression can be rewritten as 5, which is only a single term. Remember we need 2 unlike terms for a binomial |
| x2 | This expression only has 1 term. |
| x + x | This expression can be rewritten as 2x, which is only a single term. Remember we need 2 unlike terms for a binomial |
| x2 + 3x + 5 | This expression has three terms. (Not a binomial but actually a trinomial) |
