x 3 x + 3 = 8 Come play with numbers!
Expressions

Which pieces belong in the same basket?

# Like terms **Like terms** have the **same letter part** (same variables with same powers). Like: - `3x` and `5x` - `2y` and `−7y` - `4` and `9` (both constants) Not like: - `3x` and `3y` - `x` and `x²` - `2xy` and `2x` ## Combine only like terms `3x + 5x = 8x` `3x + 5y` stays `3x + 5y` > Apples with apples. `3x + 2y` is 3 apples and 2 bananas — do not smash them into 5 “appanas”. ## The matching test Two terms are like if, after you hide the coefficients, the leftover letter-part is identical. | Term | Hide coefficient | Leftover | | --- | --- | --- | | 3x | hide 3 | x | | −7x | hide −7 | x | | 4 | hide 4 | (blank — a constant) | | 2x² | hide 2 | x² | | 5xy | hide 5 | xy | `3x` and `−7x` match. `3x` and `2x²` do not. `5xy` and `5x` do not. ### Combine Only matching leftovers may share a basket. Add the hidden numbers, put the leftover back. `3x + (−7x) = −4x`

By the end of this lesson

Decide whether two terms are like, and add or subtract only like terms (3x + 5x = 8x, but 3x + 5y stays).

Remember

  • Like terms have the same letter part (same variables, same powers).
  • 3x and 5x are like. 3x and 3y are not.
  • Constants 4 and −9 are like each other (both plain numbers).
  • x and x² are unlike (different powers).
  • To combine like terms, add/subtract coefficients and keep the letter part.

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Apples with apples

Simplify 3x + 5x − x.

  1. All three terms are x-terms.
  2. Coefficients: 3 + 5 − 1 = 7
  3. Result: 7x

Answer: 7x

Check: x means 1x.

Example 2 — Leave the bananas

Simplify 4a + 3 + 2a − 1.

  1. a-terms: 4a + 2a = 6a
  2. numbers: 3 − 1 = 2
  3. 6a + 2

Answer: 6a + 2

Check: Do not write 8a or 8.

Example 3 — Spot the unlike pair

Which pair cannot combine: 2y and −9y / 2xy and 2x / 7 and 1?

  1. 2y and −9y are like → −7y
  2. 7 and 1 are like → 8
  3. 2xy and 2x are unlike — different letter parts

Answer: 2xy and 2x

Check: xy is not the same as x.

Common mistakes

Slip 3x + 2y = 5xy

Fix Unlike. Leave 3x + 2y.

You cannot smash apples and bananas into “appanas”.

Slip 3x + 5x = 8x² or 15x

Fix Add coefficients: 3+5=8, keep x. 8x.

Adding is not multiplying, and it does not raise the power.

Slip Treating x and x² as like.

Fix Different powers → unlike.

x is a box; x² is a box times itself.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

1. 7n + n =

Answer: 8n

2. 5x + 2y + x =

Answer: 6x + 2y

3. 9 − 4 + 2x =

Answer: 2x + 5

4. Are 4ab and 4a like terms?

Answer: No

Touch practice

9 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

You can add 3 apples + 2 apples, not apples + bananas.

Connect

Only matching variable names combine in code.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

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