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Pre-Algebra

Combining Like Terms

Lesson

Like terms are terms that have the exact same variable part. 3x3x and 5x5x are like terms. 3x3x and 33 are not — one has an xxand one doesn’t.

To combine like terms, add or subtract their coefficients (the numbers in front). The variable part stays the same.

  • Plain numbers (constants) are like terms with each other.
  • A variable with no number means its coefficient is 11 — so xx means 1x1x.
  • Pay attention to the sign in front of each term — it travels with the term.

Worked example 1

4x+7+2x4x + 7 + 2x

Group the like terms: the xx-terms together, constants alone:

(4x+2x)+7(4x + 2x) + 7

Combine the coefficients of the xx-terms:

6x+76x + 7

Worked example 2

3y+5y+23y + 5 - y + 2

Group yy-terms and constants:

(3yy)+(5+2)(3y - y) + (5 + 2)

Remember y-y means 1y-1y, so 3y1y=2y3y - 1y = 2y:

2y+72y + 7

How to type your answer

Write the variable term first, then the constant. No spaces needed. Use a for 1a1a and -a for 1a-1a. Examples: 8x, 6a+6, -5y+10.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

2x+3x2x + 3x

Problem 2

4yy4y - y

Problem 3

a+2a+3aa + 2a + 3a

Problem 4

6m+4m2m6m + 4m - 2m

Practice

Standard problems matching the lesson.

Problem 5

3x+5x3x + 5x

Problem 6

7y2y7y - 2y

Problem 7

6c+4c6c + 4c

Problem 8

3mm3m - m

Problem 9

4a+6+2a4a + 6 + 2a

Problem 10

5b32b5b - 3 - 2b

Problem 11

8x+43x+78x + 4 - 3x + 7

Problem 12

2y+97y+12y + 9 - 7y + 1

Problem 13

2x+52x2x + 5 - 2x

Problem 14

3a+7+5a2-3a + 7 + 5a - 2

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 15

4a2+3a5+a4a - 2 + 3a - 5 + a

Problem 16

2y+46y1-2y + 4 - 6y - 1

Problem 17

6c+3c+2c56c + 3 - c + 2c - 5

Problem 18

3x+57x+2x33x + 5 - 7x + 2x - 3

Problem 19

9m45m+7m9m - 4 - 5m + 7 - m

Problem 20

x+8+4x52x-x + 8 + 4x - 5 - 2x