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Monomial is a polynomial with one term.  Ex. -4x;   2;   2/3y;    -x/3

Binomial is a polynomial with two terms, when simplified. The terms are separated by a minus (-) or a plus(+) sign. Examples:
3x²y + 3y - 2y (this is not binomial, must be simplified)
3x²y + y (this is binomial, simplified)

-x/3 + 5
xy³ - y
5x²yz³ + 7b

Trinomial is a polynomial with three terms, when simplified,  separated by a plus (+) or minus (-) between consecutive terms.  Examples:

3xy + 2xy - y + 6  (this is not trinomial, must be simplified)
5xy - y + 6  (this is trinomial, simplified)

3yz³ + 3y + 4
-x² + 4y + z

Monomial is a polynomial with only one term. it must have one variable where the exponent is a non-negative integer, can be constant. binomial is a polynomial with two terms and trinomial has three terms........