Inputs
Enter both factors
Use x for the variable. Write x^2 or x² for powers and use implicit multiplication such as 3x.
Inputs are polynomials in x with degree 8 or lower. The output is arranged from the highest power of x to the constant term.
Math / Algebra
Polynomial Multiplication Calculator
Multiply and expand polynomials with distribution and combine-like-terms steps.
Multiply polynomialsFOILExpandLike terms
Polynomial worksheet
Result
Normalized product
x + 2 × x - 3
Expanded polynomial
x^2 - x - 6
Pairwise products
- (x) × (x) = x^2
- (x) × (-3) = -3x
- (2) × (x) = 2x
- (2) × (-3) = -6
Expansion steps
- 1
Set up the product
(x + 2)(x - 3)Write the two factors in standard polynomial notation before multiplying.
- 2
Distribute each pair
(x) × (x) = x^2Multiply the coefficients and add the exponents of x for this pair of terms.
- 3
Distribute each pair
(x) × (-3) = -3xMultiply the coefficients and add the exponents of x for this pair of terms.
- 4
Distribute each pair
(2) × (x) = 2xMultiply the coefficients and add the exponents of x for this pair of terms.
- 5
Distribute each pair
(2) × (-3) = -6Multiply the coefficients and add the exponents of x for this pair of terms.
- 6
Combine like terms
x^2 - x - 6Collect terms with the same power of x and write the final product in standard form.
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About this calculator
Method, formulas, and limits.What this does
Multiplies polynomials in x, expands products such as (x + 2)(x − 3), distributes every nonzero term, combines like terms, and returns standard form.
Who it is for
Students practicing FOIL and polynomial multiplication, educators checking worked examples, and anyone needing a transparent expansion instead of only a final expression.
How it works
Each term in the first polynomial is multiplied by each term in the second. Coefficients multiply and exponents add; the resulting terms are then collected by degree.
Limitations
Inputs are polynomials in x with degree 8 or lower and division is only allowed by constants. Functions, variables other than x, and rational expressions are not supported.
Key calculations
- Distributive Rule
- (a + b)(c + d) = ac + ad + bc + bd. Every term in one factor meets every term in the other.
- Monomial Product
- (a·x^m)(b·x^n) = (a·b)x^(m+n). Multiply coefficients and add exponents.
- Standard Form
- After distribution, combine terms with the same power of x and arrange powers from highest to lowest.
Reference ranges
- Binomial × Binomial
- Two-term factors produce four pairwise products before like terms are combined.
- Polynomial × Polynomial
- The same distributive rule works for any supported number of terms; the number of pairwise steps grows with both degrees.
- Difference of Squares
- (x + a)(x − a) simplifies to x² − a² because the two middle terms cancel.
How to use it
- 1.Enter both factorsType expressions such as x + 2, 2x² − x + 1, or (x + 1)(x − 1). Implicit multiplication is accepted.
- 2.Review the distribution listEach line shows one term from the left factor multiplied by one term from the right factor.
- 3.Combine like termsThe final step collects matching powers of x and formats the product in standard form.
FOIL is a memory aid for multiplying two binomials: First, Outside, Inside, Last. It is a special case of distributing every term in the first factor across the second.
Yes. Enter any supported polynomial in each field. The calculator lists every pairwise product and then combines like powers.
Yes. You can use x^2 or the superscript form x², along with ordinary implicit multiplication such as 3x.
Terms with the same power of x are added. If their coefficients are opposites, they cancel to zero.
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