Skill: polynomial-operations

Polynomial Operations Practice

An endless supply of never-repeating polynomial problems with instant feedback. Add, subtract, and multiply — including FOIL and the special products — one problem at a time.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Add and subtract

Combine like terms across two polynomials. The subtraction problems hide sign traps — distribute the minus to every term.

Example: (3x² + 2x − 5) + (x² − 7x + 4) → 4x² − 5x − 1

Multiply polynomials

Distribute every term to every term: monomial × polynomial, FOIL for binomial × binomial, and the box method for bigger products.

Example: (x + 4)(x − 6) → x² − 2x − 24

Special products

The two patterns worth memorizing: (a + b)² = a² + 2ab + b² and (a + b)(a − b) = a² − b².

Example: (2x + 3)² → 4x² + 12x + 9

3 Watch out for these

The three mistakes students make most often on these problems.

1. Squaring term-by-term: (x + 3)² ≠ x² + 9

Wrong: (x + 3)² = x² + 9. Right: (x + 3)² = (x + 3)(x + 3) = x² + 6x + 9 — the 2ab middle term is not optional.

2. Forgetting to distribute the minus

Wrong: (4x² − x + 3) − (x² + 2x − 8) = 3x² + x − 5. Right: the minus flips every sign: 3x² − 3x + 11.

3. Multiplying coefficients but dropping exponents

Wrong: 2x · 3x = 6x. Right: 6x² — coefficients multiply AND exponents add.

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