Expressions
Comprehensive notes, formulas, and practice questions for Expressions.
Expressions
Algebraic Expressions
What you'll learn
- To build algebraic expressions from word phrases and vice versa.
- To identify terms, coefficients, and like terms.
- To add and subtract like terms by combining coefficients.
- To evaluate an expression for given values of the variable.
Key concepts
Level 1 — Terms and like terms
Verbal: An expression is a combination of numbers, variables, and operations — no equals sign.
Symbolic: 5x + 3 has two terms: 5x and 3. The coefficient of x is 5.
Like terms: Same variable part — 4y and 7y are like; 4y and 4y² are not.
Visual:
| Expression | Terms | Like groups |
|---|---|---|
| 3a + 2b + 5a | 3a, 2b, 5a | 3a and 5a |
Level 2 — Simplifying and evaluating
Combine like terms: 3x + 5x = 8x; 7n − 2n = 5n. Constants combine separately: 4 + 9 = 13.
Phrase → expression:
| Words | Expression |
|---|---|
| 7 subtracted from m | m − 7 |
| Triple of p plus 4 | 3p + 4 |
| Product of 2 and q | 2q |
Evaluate: For x = 2, 4x² − 3 = 4(4) − 3 = 16 − 3 = 13 (Class 6: small powers only).
Worked example
Simplify 5a + 3b − 2a + 7b − 4, then find the value when a = 1, b = 2.
Step 1 — Group like terms: (5a − 2a) + (3b + 7b) − 4
Step 2 — Simplify: 3a + 10b − 4
Step 3 — Substitute: 3(1) + 10(2) − 4 = 3 + 20 − 4 = 19
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Adding unlike terms: 3x + 2y = 5xy | Treating all letters as same | Only combine like terms |
| "7 less than n" as 7 − n | Reversing order | Less than → n − 7 |
| Forgetting brackets in substitution | 2x + 3 at x = 5 done as 2×5+3 wrong order | Write 2(5) + 3 = 13 |
| Dropping the constant term | 4x + 7 simplified to 4x | Constants stay unless like constants exist |
Quick check
- Write an expression for "twice k decreased by 9."
- Simplify 8p − 3q + 2p + q.
- How many terms in 2x + 5 − 3y + x? Name them.
- Evaluate 3m − 2n when m = 4 and n = 5.
Open the Practice tab for graded questions on Algebraic Expressions.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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