Multiplying Polynomials Calculator
Multiply two polynomials in one variable and see the distribution step and the expanded answer.
Product
2x³ + 5x² − 11x + 4
- Each term distributed
- (2x²)(x + 4) + (−3x)(x + 4) + (1)(x + 4)
- Partial products
- (2x³ + 8x²) + (−3x² − 12x) + (x + 4)
- Degree of the product
- 3
The product is 2x³ + 5x² − 11x + 4.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Degree of the product | 2 + 1 | 3 |
How it works
Type the two polynomials. They must use the same letter.
Worked example
(2x² − 3x + 1)(x + 4):
- Distribute: (2x²)(x + 4) + (−3x)(x + 4) + (1)(x + 4)
- Partial products: (2x³ + 8x²) + (−3x² − 12x) + (x + 4)
- Add like terms: 2x³ + 5x² − 11x + 4
Sources
Frequently asked questions
How do you multiply polynomials?
Multiply every term of the first polynomial by every term of the second, then add the like terms. For (2x² − 3x + 1)(x + 4), the terms give 2x³ + 8x² − 3x² − 12x + x + 4, which combines to 2x³ + 5x² − 11x + 4.
What is FOIL?
FOIL is the shortcut for multiplying two binomials. Multiply the First terms, the Outer terms, the Inner terms and the Last terms, then add them. (x + 2)(x + 3) gives x² + 3x + 2x + 6, or x² + 5x + 6.
What is the degree of the product?
The degrees add. A degree 2 polynomial times a degree 1 polynomial gives a degree 3 result.
How should I type the polynomials?
Use one letter for the variable and ^ for powers, like 2x^2 - 3x + 1. Spaces do not matter. A bare number such as 5 is a polynomial too.
Can I check my answer?
Yes. Pick a number for x, such as 2, and compare the product of the two polynomials at 2 with the expanded answer at 2. They must match.