Equivalent form for Binomial Expression?

In summary, equivalent forms for binomial expressions are different ways of writing the same expression, achieved through techniques such as distribution, combining like terms, or factoring. Different binomial expressions can have the same equivalent form, as there are multiple ways to manipulate and simplify expressions. There is no standard form for equivalent binomial expressions, as it can vary depending on the techniques used. It is important to know equivalent forms for binomial expressions as it allows for easier manipulation and simplification, as well as aiding in solving equations and identifying patterns.
  • #1
eddybob123
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0
Is there a way to express ##{n\choose k}{n\choose r}## in another form without n as the "top" of the binomial coefficient? I remember seeing it once but I forgot what it was.
 
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  • #2
eddybob123 said:
Is there a way to express ##{n\choose k}{n\choose r}## in another form without n as the "top" of the binomial coefficient? I remember seeing it once but I forgot what it was.

Maybe something here will do:

http://www.cs.columbia.edu/~cs4205/files/CM4.pdf
 

1. What is an equivalent form for a binomial expression?

An equivalent form for a binomial expression is a different way of writing the same expression. This can be achieved by using the distributive property, combining like terms, or factoring.

2. How can I convert a binomial expression into an equivalent form?

To convert a binomial expression into an equivalent form, you can use algebraic techniques such as distribution, combining like terms, or factoring. You can also use the binomial theorem to expand and simplify the expression.

3. Can different binomial expressions have the same equivalent form?

Yes, different binomial expressions can have the same equivalent form. This is because there are multiple ways to manipulate and simplify an expression, resulting in different but equivalent forms.

4. Is there a standard form for equivalent binomial expressions?

No, there is no standard form for equivalent binomial expressions. The equivalent form of a binomial expression can vary depending on the techniques used to manipulate and simplify the expression.

5. Why is it important to know equivalent forms for binomial expressions?

Knowing equivalent forms for binomial expressions allows for easier manipulation and simplification of expressions. It also helps in solving equations and identifying patterns in mathematical expressions.

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