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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.
Here, you will get the simple guidelines to solve the binomial expansion of the function. Follow these simple steps and compute the function effortlessly.
Question: Find the binomial expansion of (2x+5)3?
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
= (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
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
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?
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