Expand Polynomial Calculator
This expand polynomial calculator multiplies out brackets and sorts the result by power. (2x+3)(x−4) becomes 2x² − 5x − 12, with every intermediate step and a note on special product formulas.
Source: Wikipedia – Distributivgesetz. Updated: .
How it is calculated
Expanding means multiplying every term in one bracket by every term in the other, then collecting like terms. The basis is the distributive law a(b + c) = ab + ac.
How the calculator works
For (2x+3)(x−4) the four products are 2x · x = 2x², 2x · (−4) = −8x, 3 · x = 3x and 3 · (−4) = −12. Collecting −8x + 3x = −5x gives 2x² − 5x − 12. With more than two factors the working shows how the product is built from left to right, one factor at a time. Powers such as (x+1)³ are expanded as repeated multiplication. For two binomials this is the FOIL method: first, outer, inner, last.
Special product formulas
The calculator recognises the three patterns (a + b)², (a − b)² and (a + b)(a − b) and names a and b. They save work: (x+5)² is x² + 10x + 25, and (x+5)(x−5) is x² − 25 with no middle term.
- A letter stands for a variable; xy means x times y.
- The multiplication sign may be left out: 2x, 3(x+1) and (a+b)(a−b) are valid.
- Write decimals with a point or comma, and exponents as ^2 or ².
Frequently asked questions
How do you multiply out two brackets?
Multiply each term of the first bracket by each term of the second and collect like terms. (x+2)(x+3) becomes x² + 3x + 2x + 6 = x² + 5x + 6.
What are the three special product formulas?
(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b². The calculator names the matching formula whenever the expression has that shape.
Can I use several variables?
Yes. Each letter is its own variable. (a+b)(a−c) gives a² − ac + ab − bc, ordered by degree.
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