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# Combining Like Terms

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: x2 (the 2 is the exponent, x is the base); abx(the x is the exponent, b is the base); eu (the 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

1. 15xyz
Coefficient: 15
2. -b2
Coefficient: -1 because -b2 is the same as -1b2
3. 21pq3
Coefficient: 21
4. 4ac
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

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

### Like Terms Practice #2

Find the like terms in the following expression:

x + -x2 + - x3 y2 - y +  4y4

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. 6x + 5x

2. 6y + 5y

3. 6x + 5y