Multiplying Polynomials Generator
The Multiplying Polynomials lesson covers the distributive property, FOIL, the box method, and the special product patterns in full; this generator drills the result of every one of them, asking you to evaluate a product at a chosen value or to recognize a pattern directly.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | A monomial times a binomial, evaluated at \(x\) | \(2x(6x+8)\) at \(x=-2\) |
| Medium | Two binomials (FOIL), evaluated at \(x\) | \((x+3)(x-5)\) at \(x=2\) |
| Hard | A binomial times a trinomial, or a special product pattern | \((a+b)(a-b)\) evaluated directly |
Easy multiplies a single monomial across a binomial, evaluated at a chosen \(x\) — the distributive property with small numbers.
Medium multiplies two binomials, the FOIL case, evaluated the same way.
Hard alternates between a binomial times a trinomial (the box-method case) and a special product pattern — difference of squares or a perfect square — evaluated directly on two chosen numbers instead of at \(x\).
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number — enter it exactly as computed.
- Check Answers scores the set and flags exactly which problems need another look
- Show Answers reveals every solution, useful for reviewing a paper attempt
- Print Worksheet outputs a clean page for offline practice or classroom handouts
The rules this generator drills
| Rule | Statement |
|---|---|
| Function multiplication | \((P \cdot Q)(x) = P(x) \cdot Q(x)\) |
| FOIL | First, Outer, Inner, Last — the four products of two binomials |
| Difference of squares | \((a+b)(a-b) = a^{2}-b^{2}\) |
| Perfect square | \((a+b)^{2} = a^{2}+2ab+b^{2}\) |
See the Multiplying Polynomials lesson for the full distributive-property, FOIL, and box-method technique, plus every special product pattern.
Common mistakes to watch for
Forgetting the middle term in a perfect-square pattern. \((a+b)^{2} = a^{2}+2ab+b^{2}\), not \(a^{2}+b^{2}\) — the middle term is real.
Adding exponents incorrectly during distribution. \(x \cdot x^{2} = x^{3}\), not \(x^{2}\) — this is the Product Rule from exponents, still in effect here.
Dropping a sign when a factor is negative. Every product involving a negative term needs its sign tracked as carefully as any other.
Using FOIL on more than two binomials. FOIL only covers exactly four multiplications; a binomial times a trinomial needs the box method instead.
Where to go next
Once expanding a product feels automatic, the Factoring Generator runs this exact process in reverse. For the full technique behind every problem here, see the Multiplying Polynomials lesson.