Share

## What Is The Number Of Distinct Terms In The Expansion Of (A + B + C)20?

Question

## Introduction

The number of distinct terms in the expansion of (A + B + C)20 is 10k.

## Let A = 1, B = 2 and C = 3.

Let A = 1, B = 2 and C = 3.

The expansion of (A + B + C)20 is:

(1 + 2 + 3)20 = (1 x 20) + (2 x 19) + (3 x 18).

## We can write the expansion of (A + B + C)20 as follows:

We can write the expansion of (A + B + C)20 as follows:

(A + B + C)20 = 10*10*10*10*10*10*10*10*10*10*k.

## The answer is 10k

The first step is to determine the number of distinct terms in the expansion of (A + B + C)20. Since there are three variables, A, B and C, we need three numbers that will be used as exponents during our calculations. Let’s choose 1 for A, 2 for B and 3 for C. This gives us an expression like this:

(1+2)(3+4)20 = 1*2*3*4*5*6…

## Answers ( 2 )

## What Is The Number Of Distinct Terms In The Expansion Of (A + B + C)20?

## Introduction

In mathematics, a word problem is a type of question that asks for an answer where the solution does not involve the use of basic arithmetic operations. The name comes from the Latin word probare, meaning “to test” or “to prove”. One of the most famous word problems in mathematics is called The Game of Life. It’s a 2D Conway Game, which is a type of mathematical puzzle. In this blog post, we will explore one such example: What is the number of distinct terms in the expansion of (A + B + C)20? This problem can be solved using basic algebra and simple geometric concepts. So if you are looking to brush up on your equations and geometry, read on!

## The Problem

The problem of expanding (A + B + C) is to find the total number of distinct terms. The expansion process is initiated with aterm, and each term in the expansion is created by adding another term to the original one. At first, this process seems straightforward, but as more and more terms are added, the number of possible expansions becomes incredibly large. In fact, it’s impossible to determine the exact number of expansions because there are an infinite amount of ways that terms could be combined. However, we can use a method known as counting rigorously to come up with a ballpark estimate for the total number of expansions that could take place.

Assuming that each term in the expansion has an equal probability of being chosen, the total number of possible expansions is simply ÷ 3 + 1 = 2 + 1 = 3. Therefore, there are an estimated 31 different expansions that could take place.

## The Solution

The expansion of (A + B + C) is the sum of the expansions of each term. The number of distinct terms in this expansion is 3.

## Results

The number of distinct terms in the expansion of (A + B + C) is 6.

## Conclusion

The number of distinct terms in the expansion of (A + B + C)20 is 10.

When I was in sixth grade, my teacher taught us about combinations. A combination is a group of items selected from a larger set. For example, if you have 12 fruits and want to make a fruit salad, there are many different possible combinations (permutations) of 3 fruits each morning for breakfast: 12!/(4!*2!) = 144 possible combinations. However, we usually only care about the number of distinct terms in such an expansion because some choices end up being duplicates (such as having two apples in your fruit salad). If we were calculating how many distinct terms there would be in an expansion like (a + b + c)20 (i.e., what would be the total number of ways you could choose 20 numbers out of 100), then we would only need to consider the following:

## We will start with a quick review.

Let’s review the formula for the number of terms in the expansion of (a + b + c)n:

## Let’s look at a few examples.

Example 1: The expansion of (A + B + C)20 = (1 + 2 + 3 + 4 + 5 + 6 + 7)20 = 24(A)(B)(C).

Example 2: The expansion of (A – B)20 = (-1)(-2)(-3)20 = 20(-1)(-2)(-3).

Example 3: The expansion of ((A – B)/C)20 = ((1)/2)((5)/10)((-6)/30).

## The formula for the number of terms in the expansion of (a + b + c)n is

The formula for the number of terms in the expansion of (a + b + c)n is n!/(a! a! a! … a!). The number of terms in the expansion of (a + b + c)20 is 20!, or 400,000.

## So, what is the sum of all of these terms?

So, what is the sum of all of these terms?

It’s 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 and so on…

So we can say that:

(a) The number of distinct terms in the expansion of (a+b+c)^20 = [(1+2+4)/2]^20 = [(1+2)/2]^(20*19) = (1/2)^{(20*19)}

## This formula gives us a quick way to calculate the answer.

The formula is:

$$sum_{i=0}^n {(a + b + c)^{i}} = left(frac{1}{2}a^2+frac{1}{3}b^3-frac{1}{5}right)^{n}.$$

You can use this formula to quickly calculate the number of terms in the expansion of (a + b + c)20, which is 218318800000.

We hope this has been a helpful introduction to the formula for expanding binomials. If you want to get more practice with it, check out our other blog post on calculating the number of terms in an expansion. We also have a free worksheet available if you want something simpler that can be done in class or at home!