(A+B)^n and (A-B)^n Formula Expander

(A+B) and (A-B) nth power formula expander is an online tool for algebraic operation programmed to perform formula expansion for any n-value or nth power of (A+B) and (A-B). The concept of (A+B)^n and (A-B)^n formula expander is used to describe the expression for the given nth value of formula. The binomial theorem is applied here to expand the formula. Any algebraic expression consisting of only two terms is known as a binomial expression. It’s expansion in powers of n is known as the binomial expansion. The formula by which any power of a binomial expression can be expanded in the form of a series is known as binomial theorem.
According to the theorem, it is possible to expand the power (a + b)n and (a – b)n by using Pascal’s Triangle key point. Where n is called the index of the binomial. The values of the binomial coefficients are symmetrically placed about the middle value if the index n is even, and about two middle values if the index is odd. So the same technique is used in this (A+B) and (A-B) nth Power formula calculator to expand any power of binomial (A+B) and (A-B). Refer the below table for example input & output of (A+B)n and (A-B)n calculator.

(A+B)nin WordsFormula(A+B)2A+B whole squareA2 + 2AB + B2(A+B)3A+B whole cubeA3 + 3A2B + 3AB2 + B3(A+B)4A+B whole power 4A4 + 4A3B + 6A2B2 + 4AB3 + B4(A+B)5A+B whole power 5A5 + 5A4B + 10A3B2 + 10A2B3 + 5AB4 + B5(A+B)6A+B whole power 6A6 + 6A5B + 15A4B2 + 20A3B3 + 15A2B4 + 6AB5 + B6

(A-B)nin WordsFormula(A-B)2A-B whole squareA2 – 2AB + B2(A-B)3A-B whole cubeA3 – 3A2B + 3AB2 – B3(A-B)4A-B whole power 4A4 – 4A3B + 6A2B2 – 4AB3 + B4(A-B)5A-B whole power 5A5 – 5A4B + 10A3B2 – 10A2B3 + 5AB4 – B5(A-B)6A-B whole power 6A6 – 6A5B + 15A4B2 – 20A3B3 + 15A2B4 – 6AB5 + B6