The binomial formula is used to solve the binomial expression. Binomial is a type of polynomial with exactly two terms. For example (a+b), (2+y) are some binomials. The binomial formula is used when we have to multiply a binomial by itself for ‘n’ number of times. If we want to expand a binomial expression with some higher power, then the Binomial theorem formula works well for it. Let us see the binomial formula along with solved examples in the following section.
Want to find complex math solutions within seconds?
Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps.
The binomial formula is the formula for the expansion of the multiplication of a binomial to itself n times. The binomial formula is written in the descending order of the power of the variable to avoid the confusion. Binomial Formula can be expressed as,
(a + b)n = nC0 an + nC1 an - 1 b + nC2 an-2 b2 + nC3 an - 3 b3 ................ + nCn - 1 a bn - 1 + nCn bn
(a + b)n = Σr=0nnCr an – r · br
nCr = n! ⁄ (n-r)!r!
Solved Examples Using Binomial Formula
Example 1: Using Binomial Formula, find (a + b)3.
To find: (a + b)3
Using Binomial Formula,
(a + b)n = nC0 an + nC1 a(n - 1) b + nC2 a(n - 2) b2 + nC3 a(n - 3) b3 ................ + nCn - 1 a b(n - 1) + nCn bn