Binomials

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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.