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The binomial theorem28 provides a method of expanding binomials raised to powers without directly multiplying each factor: \ ( (x+y)^ {n}=\left ( \begin {array} {c} {n} \\ [4pt] {0}\end {array}\right) x^ {n} y^ {0}+\left ( \begin {array} {c} {n} \\ [4pt] {1}\end {array}\right) x^ {n-1} y^ {1}+\left …

We begin by defining the factorial The product of all natural numbers less than or equal to a given natural number, denoted n!. of a natural number n, denoted n!, as the product of all natural numbers less than or equal to n. For example, 7! = 7 6 5 4 3 2 1 = 5,040 S e v e n f a c t o r i a l 5! = …

The binomial coefficient appears as the k th entry in the n th row of Pascal's triangle (where the top is the 0th row ). Each entry is the sum of the two above it. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

The binomial theorem is a mathematical formula that gives the expansion of the binomial expression of the form (a + b)n, where a and b are any numbers and n is a non-negative integer. According to this theorem, the expression can be expanded into the sum of terms involving powers of a and b. The …

Let us multiply a+b by itself using Polynomial Multiplication : (a+b) (a+b) = a2 + 2ab + b2 Now take that result and multiply by a+b again: (a 2 + 2ab + b 2) (a+b) = a3 + 3a2b + 3ab2 + b3 And again: (a 3 + 3a 2 b + 3ab 2 + b 3) (a+b) = a4 + 4a3b + 6a2b2 + 4ab3 + b4 The calculations get longer and …