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Combining Like Terms

Adding & Subtracting Monomials

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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

Answers:
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
Answer: 11x

2. 6y + 5y
Answer:  11y

3. 6x + 5y
Answer: 6x + 5y

For additional worksheets for simplifying the expressions (combining like terms) and using the distributive property, see the following worksheets.
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