Why only like terms combine
A term is one chunk of an expression, along with the sign in front of it. In 3x + 2y − 4, the terms are 3x, +2y and −4.
Like terms have the same letter with the same power. 3x and −5x are like terms. So are 2x² and x², and so are plain numbers like 6 and −1. The number in front of a letter has a name: the coefficient.
Here’s why only they combine. Say a bag holds 3 apples, 2 bananas and 4 more apples. If x is the price of one apple and y is the price of one banana, the bag costs 3x + 2y + 4x dollars.
The apples add up, so 3x + 4x becomes 7x. The bananas stay in their own pile, so the bag costs 7x + 2y dollars in all. Lumping it all into 9xy would be like calling the bag 9 apple-bananas.
Bottom line: sort by letter and power, then add the numbers in front. The letter part stays as it is.
Example 1: fencing a dog run
A rectangular dog run is 2x − 1 feet long and x + 4 feet wide. Write the length of fence that goes all the way around it, with like terms combined.
The working
- Add all four sides: (2x − 1) + (x + 4) + (2x − 1) + (x + 4)
- Collect the x-terms. A lone x means 1x: 2x + x + 2x + x = 6x
- Collect the plain numbers, signs included: −1 + 4 − 1 + 4 = 6
- Put the groups together: 6x + 6
- Check with x = 3. The sides are 5 and 7 feet, so the fence is 5 + 7 + 5 + 7 = 24 feet, and 6(3) + 6 = 24 too.
Answer: 6x + 6 feet
That last step works on any of these questions. Put the same number into the original and into your answer, work both out with the order of operations, and they should match.
Example 2: when x² shows up
x² means x times x, so it’s a different kind of term from x. Think of floor tiles in two sizes: you count the big squares and the long strips separately.
Which expression is equivalent to 4x² + 3x − x² + 5x − 2?
The working
- Sort by kind. The x² terms are 4x² and −x². The x-terms are 3x and 5x. The plain number is −2.
- Combine the x² terms: 4x² − x² = 3x². The −x² counts as −1x².
- Combine the x-terms: 3x + 5x = 8x
- Write the groups from the highest power down: 3x² + 8x − 2
Answer: 3x² + 8x − 2
Check with x = 2. The answer gives 12 + 16 − 2 = 26, and the original, 16 + 6 − 4 + 10 − 2, is 26 as well.
Example 3: work backward from a perimeter
Some questions give you the total and ask for a missing piece. The catch? You’ll subtract a whole group, and the minus sign has to reach every term in it.
A garden bed shaped like a triangle has a perimeter of 11x + 4 feet. Two of its sides are 3x + 2 and 4x − 1 feet. How long is the third side?
The working
- Add the two sides you know: (3x + 2) + (4x − 1) = 7x + 1
- Take that away from the perimeter. The missing side is (11x + 4) − (7x + 1)
- The minus sign flips every sign in the second group, so it becomes 11x + 4 − 7x − 1
- Combine like terms. 11x − 7x = 4x and 4 − 1 = 3, so the third side is 4x + 3.
- Check it: (3x + 2) + (4x − 1) + (4x + 3) is 11x + 4, the perimeter you started with.
Answer: 4x + 3 feet
4 mistakes that cost points
Mistake 1: adding x and x²
They look alike, but x² is a different kind of term, so 3x + 2x² stays as it is. Try x = 2: it’s 6 + 8 = 14, while 5x² would be 20.
Mistake 2: dropping a minus sign
The sign in front of a term moves with it, so in 9x + 4 − 6x the x-terms make 3x. A minus in front of parentheses flips every sign inside, so −(2x − 5) becomes −2x + 5.
Mistake 3: adding a number to a letter term
3x + 2 can’t be shortened, because the 2 has no x. Try x = 10: 3x + 2 is 32, but 5x would be 50.
Mistake 4: forgetting the invisible 1
A letter on its own has a 1 in front: x is 1x. So x + 4x is 5x, and 6y − y is 5y. Write the 1 in if it helps you see it.
Practice: 5 new questions
Every set is new. Check each answer as you go, and read the working on any you miss before the next one.
Combining like terms: 5 questions
- Questions
- 5
- Timer
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- No calculator
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New questions every time you start. Do this set as many times as you like.
- Check each answer as you go and read the working before the next question.
- The formula sheet and calculator sit in the toolbar, as they do on the real test.
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Want more? Practice all of expressions and polynomials (25 questions, every skill in the topic), or take the full GED math practice test.
Frequently asked questions
What are 5 examples of like terms?
Here are five pairs: 4x and −9x, y and 6y, 2x² and x², 3xy and −5xy, and the plain numbers 8 and −2. Each pair has the same letters with the same powers. The order of the letters makes no difference, so 2xy and 7yx are like terms too.
How do you combine similar terms?
Similar terms is another name for like terms. The steps are the same: add or subtract the numbers in front, and keep the letter part. Fractions and decimals follow the same rule. ½x + ¼x is ¾x, because ½ + ¼ = ¾, and 1.5y + 0.25y is 1.75y.
Keep going
PEMDAS: the order of operations
The order to follow when you plug a number in to check your answer.
Point-slope form
Turning y − 5 = 3(x − 2) into y = 3x − 1 ends with combining like terms.
Equations and inequalities practice
Solving an equation starts with tidying each side, and that's combining like terms.
Free printable practice test
Two full tests on paper, with a worked solution for every question.
Written by
Coach Crissy
Math instructor
Coach Crissy teaches the video lessons behind the BooknBoost GED math course, working through GED-style problems on camera: ratios and proportions, percent and interest, mean, median and mode, slope, and the geometry students meet on test day.