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Binomial Expansion Calculator

By taking the help of Binomial Expansion Calculator, you will get the accurate solution for your expression as early as possible. You have to enter input expression at the specified input box and press on the calculate button to obtain the binomial expression within no time.

Binomial Expansion Calculator: Study the process to solve the binomial expansion of the given expression. Our online handy Binomial Expansion Calculator tool is designed to help the students who wants to escape from the difficult mathematical calculations. You can know the detailed explanation of solving the binomial expansion with the best examples in the below sections.

Step By Step Procedure to Find Binomial Expansion

Here, you will get the simple guidelines to solve the binomial expansion of the function. Follow these simple steps and compute the function effortlessly.

  • Take any function to get the binomial expansion.
  • The binomial expansion formula is given by (a+b)n = ∑ k=0 to n (n!/(n-k)! k!) an-k bk.
  • Where n! = 1x2x3x4. . n.
  • Substitute the expression (a+b)n to get the a, b, n values.
  • Now, calculate the product for every value of k from 0 to n.
  • Add those obtained expressions to get the binomial expansion.

Example

Question: Find the binomial expansion of (2x+5)3?

Answer:

Given function is (2x+5)3

Binomial Expansion Formula is

(a+b)n = ∑ k=0 to n (n!/(n-k)! k!) an-k bk.

a = 2x, b = 5, n = 3.

So, (2x+5)3 = ∑ k=0 to 3 (3!/(3-k)! k!) (2x)3-k (5)k.

Calculate every value of k from 0 to 3.

For k = 0,

= (3!/(3-0)! 0!) (2x)3-0 (5)0

= 8x3

= (3!/(3-1)! 1!) (2x)3-1 (5)1

= (6/2) 4x2 * 5

= 60 x2

For k = 2,

= (3!/(3-2)! 2!) (2x)3-2 (5)2

= (6/1) (2x)1 * 25

= 150x

For k = 3,

= (3!/(3-3)! 3!) (2x)3-3 (5)3

= (2x)0 * 125 = 125

Sum up all those values

(2x+5)3 = 8x3 + 60 x2 + 150x + 125

Binomial Expansion Calculator

FAQs on Binomial Expansion Calculator

1. What is binomial example?

Binomial is a math term having two expressions connected by a plus or minus sign. An example of binomial is x + y.

2. What is binomial expansion formula?

The formula to compute the binomial expansion is (x+y)n = ∑ k=0 to n (n!/(n-k)! k!) xn-k yk.

3. How do you define binomial expansion?

A polynomial with two terms is known as binomial. Binomial expansion of the given term is defined by the binomial theorem. A binomial theorem is a mathematical theorem which gives the expansion of a binomial when it is raised to the positive integral power.

4. Calculate the binomial expansion of (x+1)4?

(x+1)4 = ∑ k = 0 to 4 (4!/(4-k)! k!) x4-k.

= (4!/(4-0)! 0!) x4-0 + (4!/(4-1)! 1!) x4-1 + (4!/(4-2)! 2!) x4-2 + (4!/(4-3)! 3!) x4-3 + (4!/(4-4)! 4!) x4-4

= (24/24 )x4 + (24/6) x3 + (24/2*2) x2 + (24/6) x1 + (24/0) x0

(x+1)4 = x4 + 4x3 + 6x2 + 4x + 1

5. Where can I find Best Tools for Binomial Expansion?

You can find the free online tools for Binomial Expansion taking the help from Onlinecalculator.guru a trusted and genuine site.