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11.7: Binomial Theorem
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/11%3A_Sequences_Probability_and_Counting_Theory/11.07%3A_Binomial_Theorem
A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consumi...A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find $(x+y)^n$ without multiplying the binomial by itself $n$ times.
11.6: Binomial Theorem
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/11%3A_Sequences_Probability_and_Counting_Theory/11.06%3A_Binomial_Theorem
A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consumi...A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find $(x+y)^n$ without multiplying the binomial by itself $n$ times.
11.6: Binomial Theorem
https://math.libretexts.org/Courses/Truckee_Meadows_Community_College/TMCC%3A_Precalculus_I_and_II/Under_Construction_test2_11%3A_Sequences_Probability_and_Counting_Theory/Under_Construction_test2_11%3A_Sequences_Probability_and_Counting_Theory_11.6%3A_Binomial_Theorem
A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consumi...A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find $(x+y)^n$ without multiplying the binomial by itself $n$ times.
11.7: Power Series
https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/11%3A_A_-_Calculus_Review_-_What_Do_I_Need_to_Know_From_Calculus%3F/11.07%3A_The_Binomial_Expansion
Another example of an infinite series that the student has encountered in previous courses is the power series. Examples of such series are provided by Taylor and Maclaurin series.
11.7: Binomial Theorem
https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/11%3A_Sequences_Probability_and_Counting_Theory/11.07%3A_Binomial_Theorem
A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consumi...A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find $(x+y)^n$ without multiplying the binomial by itself $n$ times.
8.8: The Binomial Expansion
https://math.libretexts.org/Bookshelves/Differential_Equations/A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers_(Herman)/08%3A_Appendix_Calculus_Review/8.08%3A_The_Binomial_Expansion
Another series expansion which occurs often in examples and applications is the binomial expansion.
5.1: Counting
https://math.libretexts.org/Courses/Mount_Royal_University/Mathematical_Reasoning/5%3A_Basic_Concepts_of_Probability/5.1%3A_Counting
Most of us think that counting is easy is 1,2,3.... When counting objects, one needs to careful on not counting more than once and missing an objects. In this section, we explore some ideas behind co...Most of us think that counting is easy is 1,2,3.... When counting objects, one needs to careful on not counting more than once and missing an objects. In this section, we explore some ideas behind counting.
11.8: The Binomial Expansion
https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/11%3A_A_-_Calculus_Review_-_What_Do_I_Need_to_Know_From_Calculus%3F/11.08%3A_Problems
Another series expansion which occurs often in examples and applications is the binomial expansion. This is simply the expansion of the expression (a+b)ⁿ in powers of a and b. We will investigate ...Another series expansion which occurs often in examples and applications is the binomial expansion. This is simply the expansion of the expression (a+b)ⁿ in powers of a and b. We will investigate this expansion first for nonnegative integer powers n and then derive the expansion for other values of n.
5.6: Binomial Theorem
https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus_(2e)/05%3A_Sequences_Summations_and_Logic/5.06%3A_Binomial_Theorem
This section introduces the Binomial Theorem, which provides a formula for expanding expressions of the form $(a + b)^n$ . It explains how to use binomial coefficients and Pascal’s Triangle to dete...This section introduces the Binomial Theorem, which provides a formula for expanding expressions of the form $(a + b)^n$ . It explains how to use binomial coefficients and Pascal’s Triangle to determine the terms of the expansion. Examples demonstrate how to apply the theorem to simplify polynomial expressions and solve problems involving binomial expansions.
1.11.7: Binomial Theorem
https://math.libretexts.org/Workbench/Book-_Precalculus_I_for_Highline_College_w/Rational_Inequalities_and_Equations_of_Circles/1.11%3A_Sequences_Probability_and_Counting_Theory/1.11.07%3A_Binomial_Theorem
A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consumi...A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find $(x+y)^n$ without multiplying the binomial by itself $n$ times.
25.2: Binomial Expansion
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/25%3A_The_Binomial_Theorem/25.02%3A_Binomial_Expansion
Note that the exponents of the $a$ ’s and $b$ ’s for each term always add up to $6$ , and that the exponents of $a$ decrease from $6$ to $0$ , and the exponents of $b$ increase from $0$ to...Note that the exponents of the $a$ ’s and $b$ ’s for each term always add up to $6$ , and that the exponents of $a$ decrease from $6$ to $0$ , and the exponents of $b$ increase from $0$ to $6$ . Note in particular, that the $k$ th term has a power of $b$ given by $b^{k-1}$ (and not $b^k$ ), it has a binomial coefficient $\dbinom{n}{k-1}$ , and the exponents of $a$ and $b$ add up to $n$ .

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