分解因式:x^3+4x^2y-y^3-4xy^2

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/22 17:41:39
分解因式:x^3+4x^2y-y^3-4xy^2分解因式:x^3+4x^2y-y^3-4xy^2分解因式:x^3+4x^2y-y^3-4xy^2x^3+4x^2y-y^3-4xy^2=(x³

分解因式:x^3+4x^2y-y^3-4xy^2
分解因式:x^3+4x^2y-y^3-4xy^2

分解因式:x^3+4x^2y-y^3-4xy^2
x^3+4x^2y-y^3-4xy^2
=(x³-y³)+(4x²y-4xy²)
=(x-y)(x²+xy+y²)+4xy(x-y)
=(x-y)(x²+5xy+y²)

x^3+4x^2y-y^3-4xy^2
=(x^3-y^2)+(4x^2y-4xy^2)
=(x-y)(x^2+xy+y^2)+4xy(x-y)
=(x-y)(x^2+5xy+y^2)

x³+4x²y-y³-4xy²
=x³-y³+4xy(x-y)
=(x-y)(x²+xy+y²)+4xy(x-y)
=(x-y)(x²+5xy+y²)