Binomial

The definition of a binomial is a reduced expression of two terms.

Examples of a binomial are

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.

Non examples of a binomial are

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)

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