Help with expansion of an expression

In summary, to expand an expression, you can use the distributive property, FOIL method, or the binomial theorem. The purpose of expanding an expression is to simplify it and make it easier to work with. You can expand an expression with variables using the same methods as with numbers. When expanding an expression, it is important to follow rules such as the commutative, associative, and distributive properties, as well as the exponent rules for variables. To ensure that you have expanded an expression correctly, you can simplify the expanded expression and compare it to the original expression. They should be equivalent if the expansion was done correctly.
  • #1
sliorbra
10
0
Hello,

I have a problem to understand how the author made the following expansion:


1/sqrt{1+[2(r-r')*d]/(r-r')^2}≈1-{[(r-r')*d]/(r-r')^2+...}

where all the letters go for vectors and the symbol '*' is the dot product.
I suppose it is a Taylor expansion, but i just don't get it in this case.


Can someone give me the way?
 
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  • #2
1/sqrt(1+x) ≈ 1/(1+x/2) ≈ 1-x/2
Two taylor expansions up to the linear term.
 
  • #3
thank you!
 

1. How can I expand an expression?

To expand an expression, you can use the distributive property, FOIL method, or the binomial theorem. The method you use will depend on the specific expression you are trying to expand.

2. What is the purpose of expanding an expression?

Expanding an expression allows you to simplify it and make it easier to work with. It also helps you to see the different terms and factors within the expression.

3. Can I expand an expression with variables?

Yes, you can expand an expression with variables. Just like with numbers, you can use the distributive property, FOIL method, or the binomial theorem to expand expressions with variables.

4. Are there any rules I need to follow when expanding an expression?

Yes, there are some rules you should follow when expanding an expression. These include the commutative, associative, and distributive properties, as well as the exponent rules for variables.

5. How do I know if I have expanded an expression correctly?

To check if you have expanded an expression correctly, you can simplify the expanded expression and compare it to the original expression. They should be equivalent if you have expanded it correctly.

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