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CALCULATE

CALCULATE

** (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)

(A+B)^{n} | in Words | Formula |
---|---|---|

(A+B)^{2} | A+B whole square | A^{2} + 2AB + B^{2} |

(A+B)^{3} | A+B whole cube | A^{3} + 3A^{2}B + 3AB^{2} + B^{3} |

(A+B)^{4} | A+B whole power 4 | A^{4} + 4A^{3}B + 6A^{2}B^{2} + 4AB^{3} + B^{4} |

(A+B)^{5} | A+B whole power 5 | A^{5} + 5A^{4}B + 10A^{3}B^{2} + 10A^{2}B^{3} + 5AB^{4} + B^{5} |

(A+B)^{6} | A+B whole power 6 | A^{6} + 6A^{5}B + 15A^{4}B^{2} + 20A^{3}B^{3} + 15A^{2}B^{4} + 6AB^{5} + B^{6} |

(A-B)^{n} | in Words | Formula |
---|---|---|

(A-B)^{2} | A-B whole square | A^{2} - 2AB + B^{2} |

(A-B)^{3} | A-B whole cube | A^{3} - 3A^{2}B + 3AB^{2} - B^{3} |

(A-B)^{4} | A-B whole power 4 | A^{4} - 4A^{3}B + 6A^{2}B^{2} - 4AB^{3} + B^{4} |

(A-B)^{5} | A-B whole power 5 | A^{5} - 5A^{4}B + 10A^{3}B^{2} - 10A^{2}B^{3} + 5AB^{4} - B^{5} |

(A-B)^{6} | A-B whole power 6 | A^{6} - 6A^{5}B + 15A^{4}B^{2} - 20A^{3}B^{3} + 15A^{2}B^{4} - 6AB^{5} + B^{6} |