Binomial Expansion problems Please help me

In summary, the conversation is about binomial expansion problems. The first question is asking for an explanation of the process for expanding (3X +4)^4. The second question is asking for the first 4 terms of the binomial expansion of (3x+4)^4 in descending order, and the person is wondering if there is an easier way to do this. The third question is asking for the expansion of (root3 - 2)^6 using binomial expansion. The conversation ends with someone adding that the neat thing about binomial expansion is that the coefficients are the same in reverse order, and another person giving a tip for finding the binomial expansion.
  • #1
saltrock
67
0
Binomial Expansion problems!Please help me ASAP!

1)Using binomial expand (3X +4)^4.can you please kindly explain your process.
2)Use the first 4 terms in the binomial expansion of (3x+4)^4 in the DESCENDING order of x to determine the approx. of 1.004^12.Can you please give me the way how to tackle a problem with descending powe.I know how to do ascending.IF it says first 3 terms in the ascending order i can easily get it by using the formula but if it is like ,'find the expansion of(>>blah blah)^20 in descending order,does this mean that we have to find the values all the way to 20 and get the last 3 terms or is there any easier way to do it?
3)EXpand using binomial expansion
( root3 - 2)^6

I'd like to thank in advance if anyone can help me do this.cheers.
 
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  • #2
The really neat thing about the binomial expansion is that the binomial coefficients are the same in reverse order as in the forward direction, i.e. the first and last are equal, the second and next to last are equal and so on.
 
  • #3
Tide is right here. Let me add this : if you want to calculate a binomial expansion just look at the general formule and try to "fit" the given data into this formula. Then just apply the definition (the expansion) and the only thing you need to calculate are the coefficients using the combinatorics...

regards
marlon
 

1. What is the binomial expansion formula?

The binomial expansion formula is (a + b)^n = a^n + nC1 * a^(n-1)b + nC2 * a^(n-2)b^2 + ... + nCr * a^(n-r)b^r + ... + b^n, where a and b are constants and n is a positive integer.

2. How do you expand a binomial expression?

To expand a binomial expression, you can use the binomial expansion formula or Pascal's triangle. Simply plug in the values of a, b, and n into the formula or use the corresponding row of Pascal's triangle to find the coefficients for each term.

3. How do you find a specific term in a binomial expansion?

To find a specific term in a binomial expansion, you can use the formula (nCr * a^(n-r)b^r) where n is the power of the binomial, r is the term number, and a and b are the constants. You can also use Pascal's triangle to find the coefficient for the term and then multiply it by the corresponding powers of a and b.

4. Can binomial expansion be used for non-integer powers?

Yes, binomial expansion can be used for non-integer powers as long as the power n is a positive integer. In this case, the formula becomes (a + b)^n = a^n + nC1 * a^(n-1)b + nC2 * a^(n-2)b^2 + ... + nCr * a^(n-r)b^r + ... + nCn * a^0b^n.

5. What are some real-world applications of binomial expansion?

Binomial expansion is commonly used in probability and statistics to calculate the chances of certain outcomes in events with multiple trials. It is also used in finance and economics to calculate the expected returns or losses in investments. Additionally, it is used in engineering and science to model and predict complex systems and phenomena.

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