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Binomial Expansion Calculator
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The binomial theorem is used to expand the binomials expression to any given power without direct multiplication. Binomial Expansion Calculator (Binomial Theorem Calculator) is an online tool which takes a binomial expression and expands it and gives you the answer. It is also called as binomial series calculator as it  expands the binomial expression to any power series. This is a tool that expand each binomial calculator. You just have to enter the binomial term and its power term to get its expanded form instantly.

Below is given a default binomial expression with its power, click "EXPAND". You can see that it will expand the expression by using binomial formula with respect to its appropriate power series.

## Steps for Binomial Expansion calculator

Step 1 :

Observe the given binomial expression and exponent.

Step 2 :

Apply the formal expression of the binomial theorem:

(a + b)n = $\sum_{k = 0}^{n}$ $\frac{n!}{(n - k)! k!}$ an - k bk

## Problems on Binomial Expansion calculator

1. ### Expand: (x + 2)6

Step 1 :

Given that: a = x, b = 2 and n = 6

Step 2 :

(x + 2)6 = x6 + $\frac{6 \times 2 \times x^{5}}{1!}$  + $\frac{6 \times 5 \times x^{4} \times 2^{2}}{2!}$  + $\frac{6 \times 5 \times 4 \times x^{3} \times 2^{3}}{3!}$ + $\frac{6 \times 5 \times 4 \times 3 \times x^{2} \times 2^{4}}{4!}$ + $\frac{6 \times 5 \times 4 \times 3 \times 2 \times x^{1} \times 2^{5}}{5!}$ + 26
=> x6 + 12x5 + 60x4 + 160x3 + 240x2 + 192x + 64

(x + 2)6 = x6 + 12x5 + 60x4 + 160x3 + 240x2 + 192x + 64

2. ### Expand: (y + 4)6

Step 1 :

Given that: a = y, b = 4 and n = 6

Step 2 :

(y + 4)6 = y6 + $\frac{6 \times 4 \times y^{5}}{1!}$  + $\frac{6 \times 5 \times y^{4} \times 4^{2}}{2!}$  + $\frac{6 \times 5 \times 4 \times y^{3} \times 4^{3}}{3!}$ + $\frac{6 \times 5 \times 4 \times 3 \times y^{2} \times 4^{4}}{4!}$ + $\frac{6 \times 5 \times 4 \times 3 \times 2 \times y^{1} \times 4^{5}}{5!}$ + 46
=> y6 + 24y5 + 240y4 + 1280y3 + 3840y2 + 6144y + 4096