Binomial theorem is described as the algebraic expansion of powers of a binomial in the form (x + y)ⁿ. According to the theorem we can expand (x + y)ⁿ into a sum involving terms of the form ax^by^c, where the coefficient of each term is a positive integer

(x + y)⁴  =  x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴

The most commonly used expressions are

              (x + y)²  =  x² + 2xy + y²

              (x + y)³  =  x³ + 3x²y + 3xy² + y³

             (x + y)⁴  =  x⁴ + 4x³y + 6x²y² + 4xy³ + y4

             (x + y)⁵  =  x⁵ + 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴ + y⁵

            (x + y)⁶  =  x⁶ + 6x⁵y + 15x⁴y² + 20x³y³ + 15x²y⁴ + 6xy⁵ + y⁶

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