### binomial theorem

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What is the binomial theorem formula?
Sections: The formulas, Worked examples. The Binomial Theorem is a quick way (okay, it's a less slow way) of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression (3x – 2)10 would be very painful to multiply out by hand.

What does the binomial theorem state?
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. ...

The coefficient a in the term of a x
b yc is known as the binomial coefficient or (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle.

Why do we use binomial theorem?
Economists used binomial theorem to count probabilities that depend on numerous and very distributed variables to predict the way the economy will behave in the next few years. To be able to come up with realistic predictions, binomial theorem is used in this field.

What does R mean in binomial expansion?
a is the first term of the binomial and its exponent is n - r + 1, where n is the exponent on the binomial and r is the term number. b is the second term of thebinomial and its exponent is r - 1, where r is the term number. Example 8: Find the fourth term of the expansion . Simplify the result.

How do you find the binomial?
To get any term in the triangle, you find the sum of the two numbers above it. Each row gives the coefficients to (a + b)n, starting with n = 0. To find the binomialcoefficients for (a + b)n, use the nth row and always start with the beginning.

What is binomial in science?
The binomial nomenclature system combines two names into one to give all species unique scientific names. The first part of a scientific name is called the genus. The second part of a species name is the specific epithet.

What is the constant term in a binomial expansion?
If this general term is a constant term, then it should not contain the variable x. Let us write the general term of the above binomial. Now for this term to be theconstant term, x3−r should be equal to 1.

What is nCr math?
Factorial is used to compute permutations (nPr) and combinations (nCr). A factorial is the result of multiplying a given number of consecutive integers from 1 to the given number. It is written with the exclamation sign: n! and it is defined as. 0! =

What is K in the binomial theorem?
The coefficients of the terms in the expansion are the binomial coefficients (nk) . The theorem and its generalizations can be used to prove results and solve problems in combinatorics, algebra, calculus, and many other areas of mathematics. 