In Algebra, a **term, **or** monomial, **is comprised of a combination of one to three of the following: numbers, variables, and exponents. In Algebraic expressions and equations, terms are separated by addition and subtraction signs.

**Numbers**: Constant, known quantities that remain fixed.

Examples: 100, 23, -157, π**Variables**: Symbols that represent unknown quantities.

Examples:*θ, x*,*y*, and any other letter of the alphabet**Exponents**: A known or unknown quantity that raises a base to a given power.

Examples:*x*^{2}(the 2 is the exponent,*x*is the base);*ab*(the^{x}*x*is the exponent,*b*is the base);*e*(the^{u}*u*is the exponent)

Each monomial has a coefficient, which is the number that is multiplied by the other elements of the term.

**Quick tip for finding the coefficient: **It’s usually the number at the beginning of the monomial.

### Examples of Monomials

- 15
*xyz*

Coefficient: 15 - -
*b*^{2}

Coefficient: -1 because -*b*^{2}is the same as -1*b*^{2} - 21
*pq*^{3}

Coefficient: 21 - 4
*ac*

Coefficient: 4

When monomials, or terms, share the same variable and same exponent, they are like terms. **Note:** Like terms don't have to share the same coefficient.

### Like Terms Practice #1

Find the like terms in the following expression:

x+ 2y+ 3y+ 3x+ 15y

Answers:*x* and 3*x* are like terms.

2*y*, 3*y*, and 15*y* are like terms.

### Like Terms Practice #2

Find the like terms in the following expression:

x+ -x^{2 }+ -x^{3 }+y^{2}-y+ 4y^{4}

None of these terms are alike because of different variables and exponents.

### Combining Like Terms

When **combining like terms**, or **adding and subtracting monomials**, remember that the variables and exponents must be the same.

I love shopping at the grocery store in the summer because of the delectable fruit. Below is a depiction of how I tally the peaches and plums that I buy.

- 6 peaches + 5 peaches = 11 peaches
- 16 plums + 5 plums = 21 plums
- 6 peaches + 5 plums = 6 peaches + 5 plums

Notice that 6 peaches plus 5 plums does not equal 11 peaches. Also notice that 6 peaches plus 5 plums does not equal 11 plums.

Counting peaches and plums is similar to adding and subtracting monomials.

### Like Terms Practice #4

Simplify the following expressions. (In other words: Combine like terms.)

1. 6*x* + 5*x*

Answer: 11*x*

2. 6*y* + 5*y*

Answer: 11*y*

3. 6*x* + 5*y*

Answer: 6*x* + 5*y*