Is this correct please - Binomial Theorem

In summary, the Binomial Theorem is a mathematical formula used to expand a binomial expression raised to any positive integer power. The formula for the Binomial Theorem is (a + b)^n = ∑(nCr)(a^(n-r))(b^r), and it is significant because it simplifies the process of expanding binomials without using the distributive property multiple times. A binomial expression has two terms, while a binomial coefficient is the numerical coefficient in front of each term. The Binomial Theorem has practical applications in fields such as probability, engineering, finance, and physics, allowing for the solving of problems and prediction of real-world phenomena.
  • #1
Natasha1
493
9
I'm a complete beginner at these:

(3n+1)^3 = (3n)^3 + 3(3n)^2 + 3(3n)^2 + 1

which would give me

= 3 (9n^3 + 6n^2) +1 is this correct?
 
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  • #2
anyone :confused: ??
 
  • #3
No, that is not correct.
(3n)^3 + 3(3n)^2 + 3(3n)^2 + 1
Your exponents should go from 3 down to 0.
3 (9n^3 + 6n^2) +1
This is also not correct.
 
  • #4
Natasha1 said:
I'm a complete beginner at these:

(3n+1)^3 = (3n)^3 + 3(3n)^2 + 3(3n)^2 + 1
Perhaps it is a typo but you should not have "^2" twice.

which would give me

= 3 (9n^3 + 6n^2) +1 is this correct?
You have added 3(3n)^2 and 3(2n)^2 but the second shouldn't be squared.
 
  • #5
thanks :-)
 

FAQ: Is this correct please - Binomial Theorem

What is the Binomial Theorem?

The Binomial Theorem is a mathematical formula that allows us to expand a binomial expression raised to any positive integer power.

What is the formula for the Binomial Theorem?

The formula for the Binomial Theorem is (a + b)^n = ∑(nCr)(a^(n-r))(b^r), where a and b are constants, n is the power, and nCr is the combination of n and r.

What is the significance of the Binomial Theorem?

The Binomial Theorem is significant because it allows us to easily and quickly expand binomial expressions to any power without having to repeatedly use the distributive property.

What is the difference between a binomial expression and a binomial coefficient?

A binomial expression is an algebraic expression with two terms, while a binomial coefficient is the numerical coefficient that appears in front of each term in the expansion of a binomial expression.

How is the Binomial Theorem used in real life?

The Binomial Theorem has applications in various fields, such as probability and statistics, engineering, finance, and physics. It is used to solve problems related to combinations, permutations, and probabilities, as well as to model and predict real-world phenomena.

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