Multiplying Polynomials Practice Problems (FOIL)
The distributive property, FOIL, the box method, and the special product patterns are all covered in the Multiplying Polynomials lesson. Here, each one gets tested directly — evaluate a product at a chosen value, or recognize a pattern on sight.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | A monomial times a binomial, evaluated at | |
| Medium | Two binomials (FOIL), evaluated at | |
| Hard | A binomial times a trinomial, or a special product pattern |
Easy multiplies a single monomial across a binomial, evaluated at a chosen
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
Worked examples
One example at each difficulty level, solved the way the practice set expects.
Easy. Evaluate
Distribute:
Medium. Evaluate
FOIL gives
Hard. Evaluate
Multiply each term of the binomial by the whole trinomial:
Using the practice problems
Set your preferred difficulty and count, and a fresh batch of problems appears at once. Every answer here is a whole number — enter it exactly as computed.
- Check Answers verifies every entry and highlights the ones that still need fixing
- Show Answers shows the full set of solutions, useful when grading printed copies
- Print Worksheet arranges the set into a printable page, useful for classroom handouts
The rules these practice problems drill
| Rule | Statement |
|---|---|
| Function multiplication | |
| FOIL | First, Outer, Inner, Last — the four products of two binomials |
| Difference of squares | |
| Perfect square |
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.
Adding exponents incorrectly during distribution.
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 Practice Problems runs this exact process in reverse. For the full technique behind every problem here, see the Multiplying Polynomials lesson.