Newton’s Binomial Theorem

Newton’s Binomial Theorem

A formula that can be used to find the coefficient of any term in the expansion of the nth power of a binomial of the form (a + b).

The coefficients of the expansion of (a + b)\(^{n}\) can be obtained using the numbers from Pascal’s triangle.


(a + b)\(^{1}\) = (a + b)

(a + b)\(^{2}\) = a\(^{2}\) + 2ab + b\(^{2}\)

(a + b)\(^{3}\) = a\(^{3}\) + 3a\(^{2}\)b + 3ab\(^{2}\) + b\(^{3}\)

(a + b)\(^{4}\) = a\(^{4}\) + 4a\(^{3}\)b + 6a\(^{2}\)b\(^{2}\) + 4ab\(^{3}\) + b\(^{4}\)

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