Binomial Theorem

The binomial theorem is a result in algebra that gives a formula for expanding a power of a two term expression such as x plus y raised to the n. It states that when this expression is expanded, each term takes the form of a coefficient multiplied by x raised to one exponent and y raised to another, where the two exponents always add up to n. For example, x plus y raised to the fourth power expands to x to the fourth, plus four x cubed y, plus six x squared y squared, plus four x y cubed, plus y to the fourth. The coefficient of each term, known as a binomial coefficient, depends only on n and the exponent of x, and the theorem gives a systematic way to compute every one of these coefficients without multiplying the expression out term by term.