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.
−(3x − 5) becomes −3x + 5, not −3x − 5. The leading minus sign distributes across every term inside the parentheses, not just the first one.
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.
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.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Simplify: 4x + 3 − 2x + 7
A — 2x + 10. Combine like terms separately: 4x − 2x = 2x, and 3 + 7 = 10, giving 2x + 10. 2x + 4 (B) comes from subtracting the constants instead of adding them; 6x + 10 (C) comes from adding all the x-coefficients instead of subtracting where the sign calls for it.
Expand and simplify: −(2x − 5) + 3(x + 4)
A — x + 17. Distribute the leading minus sign across (2x − 5) to get −2x + 5, and distribute 3 across (x + 4) to get 3x + 12. Adding: −2x + 5 + 3x + 12 = x + 17. −x + 7 (C) comes from failing to flip the sign of −5 inside the first parentheses — the single most common slip on this item type.
Expand: (2x − 3)(x + 5) − (x − 1)²
A — x² + 9x − 16. Expand each part separately before subtracting: (2x − 3)(x + 5) = 2x² + 7x − 15, and (x − 1)² = x² − 2x + 1. Subtracting the second from the first means distributing the minus sign across all three of its terms: 2x² + 7x − 15 − x² + 2x − 1 = x² + 9x − 16. x² + 5x − 16 (B) comes from forgetting to flip the sign on the middle term when subtracting the squared binomial.
Algebraic expressions are the foundation every other Algebra subtopic builds on — a sign error here compounds into three more mistakes downstream.
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.
Move to timed sessions once sign errors stop happening. Expressions should be the fastest Algebra subtopic once the habit is automatic.
Pair expressions with polynomials and rational expressions in a mock — all three lean on the same distribution and sign-tracking skill.
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