Binomial Expansion Calculator

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A binomial is a polynomial with only two terms and binomial expansion is the form of the Binomial Theorem which describes the expansion of a binomial when raised to different powers or exponents. Binomial expansion calculator is the quick online tool very helpful in expanding any binomial expression raised to any power.

Example 1: Expand (x + 3)2 using the Binomial expansion thereom.

Binomial Theorem expansion formula: (a+b)n = ∑nk=0 (n!)/ [(n-k)! (k!)] * an-k * bk

Given (x + 3)n = 2; a = x; b = 3

For first term k=0, second term k=1, third term k=2

(x + 3)2 = [2! /( 2! * 0!)* x2 * 30] + [2!/( 1! * 1!)* x1* 31] + [2!/( 0! * 2!) * x0* 32]

(x + 3)2 = x2 + 2*3*x + 32

(x+3)2 = x2 + 6x + 9



 
Example 2: Expand (x + 2)3 using the Binomial expansion theorem.

Binomial Theorem expansion formula: (a+b)n = ∑nk=0 (n!)/ [(n-k)! (k!)] * an-k * bk

Given (x + 2)3  n = 3; a = x; b = 2

For first term k=0, second term k=1, third term k=2, fourth term k=3

(x + 2)3 = [3! /( 3! * 0!)* x3 * 20] + [3!/( 2! * 1!)* x2* 21] + [3!/( 1! * 2!) * x1 * 22]

+ [3!/( 0! * 3!) * x0 * 23]

(x + 2)3 = x3 + 6x2 + 12x + 8



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