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- https://math.libretexts.org/Courses/Coastline_College/Math_C045%3A_Beginning_and_Intermediate_Algebra_(Tran)/14%3A_Sequences_Series_and_Binomial_Theorem/14.05%3A_Binomial_Theorem\((a+b)^{n}=\left( \begin{array}{c}{n} \\ {0}\end{array}\right) a^{n}+\left( \begin{array}{c}{n} \\ {1}\end{array}\right) a^{n-1} b^{1}+\left( \begin{array}{c}{n} \\ {2}\end{array}\right) a^{n-2} b^{2...\((a+b)^{n}=\left( \begin{array}{c}{n} \\ {0}\end{array}\right) a^{n}+\left( \begin{array}{c}{n} \\ {1}\end{array}\right) a^{n-1} b^{1}+\left( \begin{array}{c}{n} \\ {2}\end{array}\right) a^{n-2} b^{2}+\ldots+\left( \begin{array}{c}{n} \\ {r}\end{array}\right) a^{n-r} b^{r}+\ldots+\left( \begin{array}{c}{n} \\ {n}\end{array}\right) b^{n}\)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/09%3A_Sequences_and_the_Binomial_Theorem/9.04%3A_The_Binomial_TheoremSimply stated, the Binomial Theorem is a formula for the expansion of quantities for natural numbers.
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_(Stitz-Zeager)_-_Jen_Test_Copy/09%3A_Sequences_and_the_Binomial_Theorem/9.04%3A_The_Binomial_TheoremSimply stated, the Binomial Theorem is a formula for the expansion of quantities for natural numbers.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/11%3A_Sequences_Probability_and_Counting_Theory/11.07%3A_Binomial_TheoremA 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.
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/09%3A_Sequences_and_the_Binomial_Theorem/9.04%3A_The_Binomial_TheoremSimply stated, the Binomial Theorem is a formula for the expansion of quantities for natural numbers.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/11%3A_Sequences_Probability_and_Counting_Theory/11.06%3A_Binomial_TheoremA 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.
- 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_TheoremA 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.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT_1320_Finite_Mathematics/05%3A_Sets_and_Counting/5.06%3A_Binomial_TheoremThe expansion \((x + y)^7 = (x + y) (x + y) (x + y) (x + y) (x + y) (x + y) (x + y) \) In multiplying the right side, each product is gotten by picking an \(x\) or \(y\) from each of the seven factors...The expansion \((x + y)^7 = (x + y) (x + y) (x + y) (x + y) (x + y) (x + y) (x + y) \) In multiplying the right side, each product is gotten by picking an \(x\) or \(y\) from each of the seven factors \((x + y) (x + y) (x + y) (x + y) (x + y) (x + y) (x + y)\). \[(x+y)^{7}=\square x^{7}+\square x^{6} y+ \square x^{5} y^{2}+ \square x^{4} y^{3}+ \square x^{3} y^{4}+\square x^{2} y^{5}+\square x y^{6}+\square y^{7} \nonumber \]
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/09%3A_Sequences_Series_and_the_Binomial_Theorem/9.04%3A_Binomial_TheoremThe binomial theorem provides a method of expanding binomials raised to powers without directly multiplying each factor.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/08%3A_Combinatorics/8.05%3A_The_Binomial_TheoremA binomial is a polynomial with exactly two terms. The binomial theorem gives a formula for expanding (x+y)ⁿ for any positive integer n .
- https://math.libretexts.org/Courses/Palo_Alto_College/College_Algebra/06%3A_Sequences_Probability_and_Counting_Theory/6.06%3A_Binomial_TheoremA 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.
