Simplifying Algebraic Expressions
Learn to combine like terms and simplify expressions
1. Understanding Like Terms
What are Like Terms?
Like terms have the same letter, or are both plain numbers. Only like terms can be combined into one term!
Example: Boxes of Clips
Mr Tan had 6 boxes of blue clips and 2 boxes of red clips. There were y clips in each box.
6y and 2y are LIKE TERMS because they both have the letter y.
Like Terms vs Unlike Terms
Like Terms (Can combine)
- • 3y and 5y → both have y
- • 2x and 7x → both have x
- • 4 and 9 → both are numbers only
Unlike Terms (Cannot combine)
- • 3x and 5y → different letters
- • 2x and 7 → one has x, one doesn't
- • 4a and 4b → different letters
Common Mistake: 2x + 7 ≠ 9x!
You cannot combine unlike terms. 2x + 7 stays as 2x + 7.
2. Adding Like Terms
To add like terms: Add the numbers in front of the letter.
6y + 2y = 8y, because 6 + 2 = 8
Example: How Many Clips Altogether?
Mr Tan had 6 boxes of blue clips (6y) and 2 boxes of red clips (2y). How many clips did he have altogether?
6y + 2y = 8y
Think: 6 boxes + 2 boxes = 8 boxes (of y clips each)
More Addition Examples
3x + 5x = 8x
4a + a = 4a + 1a = 5a (Remember: "a" by itself means "1a")
7m + 3m + 2m = 12m
Practice: Adding Like Terms
Simplify: 9p + 4p
ShowHide solution
9p + 4p = 13p
3. Subtracting Like Terms
To subtract like terms: Subtract the numbers in front of the letter.
6y - 2y = 4y, because 6 - 2 = 4
Example: How Many More Blue Clips?
Mr Tan had 6 boxes of blue clips and 2 boxes of red clips. There were y clips in each box. How many more blue clips than red clips did he have?
6y - 2y = 4y
He had 4y more blue clips than red clips.
More Subtraction Examples
10x - 3x = 7x
8n - n = 8n - 1n = 7n
15k - 6k - 4k = 5k
Practice: Subtracting Like Terms
Simplify: 12q - 5q
ShowHide solution
12q - 5q = 7q
4. Combining Letter Terms and Numbers
The Rule
When you have letter terms AND numbers:
- Combine the letter terms together
- Add or subtract the plain numbers together
- The sign in front of a term moves with it
- We usually write the letter term first (8y + 7), but 7 + 8y is also correct
Example: Clips Plus Extras
Mr Tan had 6 boxes of blue clips and 2 boxes of red clips, with y clips in each box. He also found 2 extra blue clips and 5 extra red clips. How many clips did he have in the end?
Step by step:
6y + 2 + 2y + 5
= (6y + 2y) + (2 + 5)
= 8y + 7
Grouping Like Terms
Group the x terms together, and the numbers together
5x + 3 - 2x + 7
= (5x - 2x) + (3 + 7)
= 3x + 10
More Examples
Example 1:
4a + 7 - 3a + 5
= (4a - 3a) + (7 + 5)
= a + 12
Note: 4a - 3a = 1a, and we write 1a as a
Example 2:
7m + 3 + 2m - 1
= (7m + 2m) + (3 - 1)
= 9m + 2
Example 3:
10n - 4 - 3n + 9
= (10n - 3n) + (9 - 4)
= 7n + 5
Note: - 4 + 9 is the same as 9 - 4 = 5
Practice: Combining Terms
Simplify: 8k + 5 - 3k + 2
ShowHide solution
8k + 5 - 3k + 2
= (8k - 3k) + (5 + 2)
= 5k + 7
Practice: Word Problem
Box A has x cherries. Box B has 3 times as many cherries as Box A. Box C has 9 cherries. Express the total number of cherries in all 3 boxes in terms of x.
ShowHide solution
Box A = x
Box B = 3x
Box C = 9
Total = x + 3x + 9 = 4x + 9
Common Mistakes to Avoid
Mistake 1: Adding unlike terms
Wrong: 2x + 7 = 9x
Correct: 2x + 7 (cannot simplify further)
Mistake 2: Writing the letter twice
Wrong: 3x + 2x = 5xx
Correct: 3x + 2x = 5x
Mistake 3: Leaving the answer as 1x
Not fully simplified: 4x - 3x = 1x
Correct: 4x - 3x = x (1x is the same as x, and we write it as x)
Key Takeaways
- ✓ Like terms have the same letter (3x and 5x are like terms)
- ✓ Add like terms: 6y + 2y = 8y (add the numbers in front)
- ✓ Subtract like terms: 6y - 2y = 4y (subtract the numbers in front)
- ✓ Unlike terms cannot be combined: 2x + 7 stays as 2x + 7
- ✓ Group like terms together: 5x + 3 - 2x + 7 = 3x + 10
- ✓ A letter alone means "1 times" that letter: x = 1x