Question

What is the expression of the binomial theorem?

A.(a + b)n = 1
B.The probability of two or more events occurring simultaneously is equal to the product of their individual probabilities.
C.a + b = 1
D. 2⁴ = 16

Answer 1

The binomial theorem expresses the expansion of the power (a + b)^n into a series involving terms of the form a's power decreasing and b's power increasing, multiplied by combinatorial coefficients from Pascal's triangle.

Step-by-step explanation:

Binomial Theorem Expression

The expression of the binomial theorem is a powerful tool in mathematics that allows us to expand expressions that are raised to a power. The general form of the binomial theorem for the binomial (a + b)n is:

(a + b)n = an + nan-1b + ⅓n(n-1)an-2b2 + ⅔n(n-1)(n-2)an-3b3 + ...

The theorem continues with terms decreasing the exponent of 'a' by one and increasing the exponent of 'b' by one until 'b' is raised to the power of 'n'. Each term is also multiplied by a combinatorial factor that corresponds to the coefficients in Pascal's triangle. This expansion is used in probability theory, algebra, and many other areas of mathematics.