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Math · Algebra

Algebraic expressions

Simplify, expand, and manipulate expressions with variables — combining like terms and applying the distributive property without dropping a sign. Every question comes with a written walkthrough of exactly where a term goes missing.

Practise algebraic expressions nowSee sample questions
3
Difficulty tiers
30s
Target pace
62%
Average first-attempt score

What's covered

  • Combining like terms — group terms with the same variable and exponent; a coefficient of 1 or −1 is the easiest one to lose track of.
  • The distributive property — multiply a term across every term inside parentheses, including the sign in front of it.
  • Expanding two binomials — multiply each term in the first factor by each term in the second, then combine like terms.
  • Nested parentheses and negative signs — a minus sign in front of parentheses flips every sign inside, not just the first term.
  • Substituting values — replace every instance of the variable and respect order of operations before simplifying.

Where students lose marks

Dropping the sign on a subtracted group

−(3x − 5) becomes −3x + 5, not −3x − 5. The leading minus sign distributes across every term inside the parentheses, not just the first one.

Combining unlike terms

3x and 3x² look similar enough to merge under time pressure, but different exponents mean they aren't like terms — they can't be combined at all.

Confusing the rule for combining with the rule for multiplying

Adding coefficients (like terms) and adding exponents (multiplying powers) are two different rules that apply in two different situations — mixing them up produces a wrong answer that still looks plausible.

Three sample questions

Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.

Sample 01Foundation

Simplify: 4x + 3 − 2x + 7

Sample 02Core

Expand and simplify: −(2x − 5) + 3(x + 4)

Sample 03Advanced

Expand: (2x − 3)(x + 5) − (x − 1)²

How to practise this

Algebraic expressions are the foundation every other Algebra subtopic builds on — a sign error here compounds into three more mistakes downstream.

Rewrite before you simplify

Write out every distributed term on its own line before combining anything. Untimed practice is where that discipline sticks, before speed tempts you to skip it.

Then 30 seconds a question

Move to timed sessions once sign errors stop happening. Expressions should be the fastest Algebra subtopic once the habit is automatic.

Fold into a mock

Pair expressions with polynomials and rational expressions in a mock — all three lean on the same distribution and sign-tracking skill.

Stop losing marks to a sign.
Start tracking every term.

  • A term-by-term walkthrough on every item
  • Timed or untimed sessions, any length you like
  • Tracked separately — see your algebraic expressions accuracy and pace over time
Start practising free

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Related Math subtopics

Age, work, and mixture word problemsExponentsLinear equationsPolynomialsQuadratic equationsRadicals and radical equationsRational expressionsAll of Math