Binomials

Binomial is a sum/difference of TWO monomials.

Both monomials are called terms.

Examples of binomials are:

${5}+{x}$
${2}{{x}}^{{2}}+{{y}}^{{3}}{x}$
${10}{x}{{y}}^{{3}}-{z}{{y}}^{{2}}{x}$

Examples of expressions, that are not binomials:

${x}+\frac{{1}}{{x}}$ (second term is not a monomial)
$\frac{{{2}-{y}}}{{x}}$ (division is not allowed)
${x}{{y}}^{{2}}+{z}-{2}$ (binomial can have only TWO terms)

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

For example, in binomial ${4}{{x}}^{{2}}{{y}}^{{3}}-{9}{{z}}^{{8}}{{y}}^{{7}}$ 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 ${4}{{x}}^{{2}}{{y}}^{{3}}-{9}{{z}}^{{8}}{{y}}^{{7}}$ is 15.

Exercise 1. Determine whether the following is a binomial: $\frac{{2}}{{5}}{x}-\frac{{3}}{{5}}{y}$ ?

Answer: yes.

Exercise 2. Determine whether the following is a binomial: $\frac{{1}}{{x}}+{2}{y}+{3}$ ?

Answer: no.

Exercise 3. Determine whether the following is a binomial: $\sqrt{{{3}}}{x}\cdot{y}+{5}{z}{y}$ ?

Answer: yes.

Exercise 4. Find degree of the following expression: $-{x}{y}+{5}$ ?

Answer: 2.

Exercise 5. Find degree of the following expression: $-{{p}}^{{3}}{{q}}^{{9}}+{5}{{z}}^{{3}}{{y}}^{{4}}{{p}}^{{{10}}}$ ?

Answer: 17.