乘法公式chengfa gongshi

包括：
❶ (x+y)²＝x²+2xy+y².

❷ (x-y)²＝x²-2xy+y².

❸ (x+y)(x-y)=x²-y².

❹(x+y)³＝x³+3x²y+3xy²+y³.

❺(x-y)³＝x³-3x²y+3xy²-y³.

❻(x-y)(x²+xy+y2)=x³-y³.

❼(x+y)(x²-xy+y²)=x³+y3.

❽(x+a)(x+b)=x²+(a+b)x+ab.

❾(x₁+x₂+…+x_n)²＝x²₁+x²₂+…+x²_n+2x₁x₂+2x₁x₃+…+2x_n-1x_n.

❿ (x-y)(x^n-1+x^n-2y+…+xy^n-2+yⁿ＝xⁿ-yⁿ.
(11)(x+y)(x2k-1-x2k-2y+x2k-3y2-…-y2k)=x^2k-y^2k.
(12)(x+y)(x^2k-x^2k-1y+x^2k-2y²-…+y^2k)=x^2k+1+y^2k+1.

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乘法公式chengfa gongshi

参见 “条件概率”。