Multinomial expansion is a mathematical process of raising a polynomial to a power, resulting in an expanded polynomial with multiple terms.
Binomial expansion involves raising a polynomial with two terms to a power, while multinomial expansion involves raising a polynomial with three or more terms to a power.
The formula for multinomial expansion is (x1 + x2 + ... + xn)m = ∑i1+i2+...+in=m (m choose i1, i2, ..., in) * x1i1 * x2i2 * ... * xnin, where m is the power, n is the number of terms, and i1, i2, ..., in are non-negative integers.
Multinomial expansion is primarily used in combinatorics and probability to calculate the number of possible outcomes in a given situation. It is also useful in simplifying complicated polynomial expressions.
Yes, multinomial expansion can be used to expand polynomials with variables, as long as the variables follow the same rules as the constants in the formula. This means that variables cannot have negative exponents and must have whole number coefficients.