Binomial Expansion long division

In summary, the conversation discusses using the identity (1+2x)(1-2x+4x^2) = 1+8x^3 to expand (1-2x+4x^2)^(-0.5) in ascending powers of x, and the solution obtained through long division. The conversation also mentions the equation (1+2x)^(0.5) = 1+x-x^2/2+x^3/2+... and the correction of (1/(1+2x))^(-0.5) = (1+2x)^0.5.
  • #1
chrisyuen
56
0

Homework Statement



Using the identity (1+2x) (1-2x+4x^2) = 1+8x^3 to expand (1-2x+4x^2)^(-0.5) in ascending powers of x as far as the term in x^3. (The answer is 1+x-x^2/2-7x^3/2+...)

Homework Equations



(1+2x)^(0.5) = 1+x-x^2/2+x^3/2+...
(1+8x^3)^(-0.5) = 1-4x^3+...

The Attempt at a Solution



By long division, I have the solution of 1-x+3x^2/2-13x^3/2+...
 
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  • #2
Since you have raised (1+2x) to the power of +(0.5), you should
be multiplying, not dividing. (Easy).
 
  • #3
davieddy said:
Since you have raised (1+2x) to the power of +(0.5), you should
be multiplying, not dividing. (Easy).

Yes, I got it.

I forgot (1/(1+2x))^(-0.5) = (1+2x)^0.5.

Thank you very much!
 

FAQ: Binomial Expansion long division

What is binomial expansion long division?

Binomial expansion long division is a mathematical method used to expand a binomial expression, which contains two terms, using the principles of long division. It is used to simplify complex expressions and solve equations.

How does binomial expansion long division work?

In binomial expansion long division, the divisor is multiplied by the first term of the binomial expression, and the resulting product is subtracted from the original expression. This process is repeated until all terms of the binomial expression are used. The final result is the expanded form of the expression.

What is the purpose of using binomial expansion long division?

The purpose of using binomial expansion long division is to simplify complex expressions and solve equations. It is also used to find coefficients of binomial expansions, which are useful in probability and statistics problems.

Can binomial expansion long division be used for any type of expression?

No, binomial expansion long division can only be used for binomial expressions, which contain two terms. It cannot be used for expressions with more than two terms or expressions that contain variables with exponents greater than one.

What are some common mistakes when using binomial expansion long division?

Some common mistakes when using binomial expansion long division include forgetting to distribute the negative sign, not properly aligning the terms during the long division process, and making errors in the multiplication or subtraction steps. It is important to carefully follow the steps and check for any mistakes in order to get the correct result.

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