Question

因式分解：x的3次方-x+y的3次方-y

Answer 1

立方和公式：x³+y³=(x+y)(x²-xy+y²)

x³-x+y³-y
=(x³+y³)-(x+y)
=(x+y)(x²-xy+y²)-(x+y)
=(x+y)(x²-xy+y²-1)

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Answer 2

解: x³-x+y³-y
=(x³+y³)-(x+y) x³与y³放一起, 以应用立方和公式
=(x+y)(x²-xy+y²)-(x+y) 应用立方和公式
=(x+y)(x²-xy+y²-1) 提取公因式 x+y
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Answer 3

x³-x+y³-y
=(x³+y³)-(x+y)……………………加法结合律
=(x+y)(x²-xy+y²)-(x+y) ………… 立方和公式
=(x+y)(x²-xy+y²-1)……………… 提取公因式

Answer 4

x^3-x+y^3-y
=x^3+y^3-(x+y)
=(x+y)(x^2-xy+y^2)-(x+y)
=(x+y)(x^2-xy+y^2-1)

Answer 5