Solve Binomial Series: Quickly Answer Before Spring Break!

  • Thread starter kollo3
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In summary, the conversation is about a homework task involving expanding expressions with exponents up to the 15th power. The person is looking for an easier or faster way to do this and is asking for help before their spring break ends. The conversation mentions the use of properties of multiplication and the potential use of Newton's binomial formula to solve the task.
  • #1
kollo3
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Can Someone Plz Answer Asap!

My teacher gave me homework and i got to convert for ex. (a+b)squared=a squared+ab+b squared, i got to do this up until to the 15th power. Please anyone have an ez way to do this or a shortcut. PLZ REPLY MY SPRING BREAK IS ALMOST OVER I HAVE LIKE 3 DAYS TO DO THIS
 
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  • #2
What is your question? You need to expand

[tex](a+b)^2[/tex]

?

Just write it as

[tex](a+b)(a+b)[/tex]

and use the properties of multiplication...
 
  • #3
kollo3 said:
My teacher gave me homework and i got to convert for ex. (a+b)squared=a squared+ab+b squared, i got to do this up until to the 15th power. Please anyone have an ez way to do this or a shortcut. PLZ REPLY MY SPRING BREAK IS ALMOST OVER I HAVE LIKE 3 DAYS TO DO THIS

[tex] (a+b)^{2}=a^{2}+2ab+b^{2} [/tex] !

Now,are u interested in that

[tex] \left[(a+b)^{2}\right]^{15}=(a+b)^{30} [/tex]

,or in that

[tex] (a+b)^{15} [/tex]

Do you know something about the Newton's binomial formula ...?


Daniel.
 
  • #4
kollo3:
You know of Newton's binomial formula.
Your teacher is testing you whether you understand how to apply that formula or not.
 

Related to Solve Binomial Series: Quickly Answer Before Spring Break!

What is a binomial series?

A binomial series is a mathematical expression that represents the expansion of a binomial equation, which is an equation with two terms. It follows the form (a + b)^n, where n is a non-negative integer, and a and b are constants.

What is the purpose of solving a binomial series?

The purpose of solving a binomial series is to find the expanded form of a binomial equation. This can be useful in various mathematical and scientific applications, such as finding the coefficients of a polynomial, calculating probabilities, and solving differential equations.

How do you solve a binomial series?

To solve a binomial series, you can use the binomial theorem, which states that (a + b)^n = sum of (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This formula allows you to find the coefficients of each term in the expanded form of the binomial equation.

Is there a quick way to solve a binomial series?

Yes, there are several shortcuts or tricks that can help you solve a binomial series quickly. These include using patterns in the coefficients, using Pascal's triangle, or using the binomial theorem with specific values of a and b. With practice, you can solve binomial series efficiently and accurately without using a calculator.

What are some common mistakes to avoid when solving a binomial series?

Some common mistakes when solving a binomial series include forgetting to include negative signs, mixing up the order of the terms, or miscalculating the coefficients. It is also important to remember to use the correct values for a and b and to follow the correct steps in using the binomial theorem.

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