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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

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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

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  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



    Answer  :  

    (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



    Answer  :  

    (y + 4)6 = y6 + 24y5 + 240y4 + 1280y3 + 3840y2 + 6144y + 4096



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