公式: an−bn a^n-b^n an−bn =(a−b)(an−1b0+an−2b1+…+a1bn−2+a0bn−1 = (a-b)(a^{n-1}b^0 + a^{n-2}b^1 +…+ a^1b^{n-2} + a^0b^{n-1}=(a−b)(an−1b0+an−2b1+…+a1bn−2+a0bn−1=(a−b)(an−1+an−2b+…+abn−2+bn−1) = (a-b)(a^{n-1} + a^{n-2}b +…+ ab^{n-2} + b^{n-1} ) =(a−b)(an−1+an−2b+…+abn−2+bn−1) 其中:n为正整数. 记忆方法:此消彼长;