Math Assignment Help >> Binomial Theorem

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Binomial theorem is part of elementary algebra mathematics which describes the algebraic expansion of powers of a binomial. According to binomial theorem it is case to expand the power (x + y)ⁿ into a sum including terms in the form ax^by^c, in which the exponents b and c are considered as nonnegative integers with b + c = n, and the coefficient a for each term is a specific positive integer depending on n and b. When an exponent value is zero, then the corresponding power is usually omitted from the term. i.e.

(x+y)⁴ = x⁴+4x³y+6x²y²+4xy³+y⁴

The coefficient a in term x^by^c is called as binomial coefficient.

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Binomial Theorem Expansion (a+b)ⁿ

• Total terms involved in expansion are (n+1)

• First term is mention as aⁿ and last term is mention as bⁿ.

• In order to forward first term to last term, exponent of a decreases by 1 and the exponent of b increases by 1 and the sum of exponent of a and b is equal to n.

• The coefficient of each term which is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we find the coefficient of the next term.

Binomial Theorem Formula

For positive integer values of n