Simplifying expressions – Grade 7
Simplify expressions: collect like terms, expand brackets and handle negative signs with worked examples. Create a free worksheet or try an online test.
🎯 What you will learn
- ✓Recognise like terms
- ✓Distribute factors and signs
💡 How it works
An expression is a calculation such as 3x + 2. Without an equation, you are not finding a particular x; you are writing an equivalent expression more simply.
How it works
💡 Combine only matching variable parts: 3x + 2x = 5x, but 3x + 2 stays as it is.
The number before a variable is its coefficient. In 5x − 2x, subtract the coefficients: (5 − 2)x = 3x. A lone x means 1x. Constants form a separate group. Also, x and x² are not like terms.
Expand brackets before collecting terms. A factor applies to every term: 2(x + 3) = 2x + 6. A minus before brackets is a factor of −1, so −(x − 4) becomes −x + 4.
🧩 See the method
✍️ Worked examples
Worked examples 1
3x + 5 + 2x − 1
- 1.Variable terms: 3x + 2x = 5x.
- 2.Constants: 5 − 1 = 4.
- 3.Together: 5x + 4. At x = 2, both expressions give 14.
✓ 5x + 4
Worked examples 2
2(x + 3) − (x − 4)
- 1.First brackets: 2x + 6.
- 2.Second brackets with minus: −x + 4.
- 3.2x + 6 − x + 4 = x + 10.
✓ x + 10
⚠️ Common mistakes
- • Turning 3x + 2 into 5x: the 2 has no variable part.
- • Changing only the first sign in −(x − 4). Both terms are multiplied by −1.
📝 Try it yourself
1.
4x + 3x
Show answer
7x
2.
7a − 2a + 4
Show answer
5a + 4
3.
3(x + 2)
Show answer
3x + 6
4.
5x − (2x + 3)
Show answer
3x − 3
5.
2a + 3b + a
Show answer
3a + 3b
6.
4(x − 1) − 2(x + 3)
Show answer
2x − 10
Create matching questions
Create a compact printable worksheet or start an online test.
Learn next
FAQ
Can I combine x and x²?
No. Their variable parts differ. x + x² remains a sum.
Does substitution prove two expressions equivalent?
A single value can reveal errors but does not prove equivalence for every value. Use valid algebraic transformations.