Concepts practice

Pick a topic. Each round is a short set of multiple-choice questions with a picture-first explanation on every reveal — see why each identity is true.

Squares and powers of a sum — the whole square

Tila · Miro & Moro Count all four lots: a², b² and the two matching ab twins.

Square of a Sum — (a+b)² and the two twins 25 questions · grades 6-8 The Dreamer's Dream — why (a+b)² ≠ a²+b² 25 questions · grades 6-8 Trinomial Square — the viral 3×3 tile 25 questions · grades 6-8 Cube of a Sum — 1-3-3-1 25 questions · grades 6-8 Numbers as Shapes — mental squaring 25 questions · grades 6-8 Pascal's Rows — the coefficient triangle 25 questions · grades 6-8

(a + b)(c + d) — the box

Boxer Every pair gets its own room; add the rooms.

Table of Parts — squares of sums & the box method 25 questions · grades 6-8 Find the Rectangle — factoring by the box, run backward 25 questions · grades 6-8 The Square Garden — completing the square 25 questions · grades 6-8

Differences and cubes — the corner and the cut

Overlap Take two strips away and the corner goes twice; put it back once.

Square of a Difference — the double-counted corner 25 questions · grades 6-8 Difference of Squares — cut and slide 25 questions · grades 6-8 Cubes — sum, difference, and (a−b)³ 25 questions · grades 6-8

Is it always true? — the snip test and review

Kerf Cut anywhere, at any value; a claim that still balances is an identity.

Snip Anywhere — identities vs equations 25 questions · grades 6-8 Proof Ladder — evidence vs proof 25 questions · grades 6-8 Identity Duel — mixed review 25 questions · grades 6-8 Bảy hằng đẳng thức — the seven remarkable identities (VN Toán 8) 25 questions · grades 6-8

Every answer is checked by a deterministic engine. On-device · no accounts · nothing leaves the device.