Algebraic Expressions • Topic 1 of 4

Simplifying Expressions

Simplifying means collecting terms that are genuinely alike and applying the order of operations correctly. Only like terms combine: 3x and 5x add to 8x, but 3x and 5x² never merge because the powers differ. Coefficients add; the variable part is left untouched. When a minus sign sits in front of a bracket, it flips every term inside — −(2x − 5) is −2x + 5, and this dropped sign is the single most common slip on the whole test. Constant multipliers distribute across every term, and you should always simplify an expression fully before substituting numbers, because a tidy expression is far faster to evaluate on the basic calculator. Treat a compound chunk like (x + 1) as a single object when it repeats — 4(x + 1) − 2(x + 1) is just 2(x + 1).

✅ Solved examples

1. Simplify 5x + 3 − 2x + 7.
Group like terms: (5x − 2x) + (3 + 7) = 3x + 10.
2. Simplify 4(2a − 3) − 3(a − 5).
Distribute: 8a − 12 − 3a + 15. The −3 flips both inner signs. Combine: (8a − 3a) + (−12 + 15) = 5a + 3.
3. Simplify 3x² + 2x − x² + 5x − 4.
Combine each power separately: (3x² − x²) + (2x + 5x) − 4 = 2x² + 7x − 4.
4. If x = −2, evaluate 2(x − 4) − (3x + 1).
Simplify first: 2x − 8 − 3x − 1 = −x − 9. Then substitute: −(−2) − 9 = 2 − 9 = −7.

✏️ Practice — try these, take hints as needed

1. Simplify 7y − 2 + 3 − 4y.
Group the y-terms.
Group the constants.
(7y − 4y) + (−2 + 3).
3y + 1
2. Simplify −(3m − 7) + 2m.
The leading minus flips both signs.
−3m + 7 + 2m.
Combine the m-terms.
−m + 7
3. Simplify 2(3a + b) − 3(a − 2b).
Distribute both brackets.
6a + 2b − 3a + 6b.
Combine a-terms and b-terms.
3a + 8b
4. Simplify 4x² − 5x + x² + 5x.
Only like powers combine.
The x-terms cancel.
4x² + x².
5x²
5. If a = 3, evaluate 5(a − 1) − 2(2a + 3) after simplifying.
Distribute: 5a − 5 − 4a − 6.
Simplify to a − 11.
Substitute a = 3.
−8

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
Expanding & the FOIL Method →