Binomial theorem

Binomial theorem is a term in elementary algebra for a theorem that says it is possible to find any power of a binomial without multiplying at length.

Thus (x + y)ⁿ could be expanded into a sum involving terms of the form ax^by^c, where the exponents 'b' and 'c' are nonnegative integers with b + c = n, and the coefficient 'a' of each term is a specific positive integer depending on n and b. Please note that the binomial coefficient ( n b ) appears as the b^th entry in the n^th row of Pascal's triangle (counting starts at 0). Each entry is the sum of the two above it.

For example,
if n=0
(x+y)⁰=1
if n=1
(x+y)¹=x+y
if n=2
(x+y)²=x²+2xy+y²
if n=3
(x+y)³=x³+3x²y+3xy²+y³
if n=4,
(x+y)⁴=x⁴+4x³y+6x²y²+4xy³+y4.
if n=5,
(x+y)⁵=x⁵+5x⁴y¹+10x³y²+10x²y³+5xy⁴+y⁵

and so on.

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