问几道数学题目的分解

来源：百度知道 编辑：UC知道 时间：2024/06/05 00:50:59
x^4+x^2y^2+y^4

x^2y-7xy+6y

补充说明：x^4意思是x的4次方 依次类推

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

x^2y-7xy+6y
=y(x^2-7x+6)
=y(x-1)(x-6)

=(X^2+Y^2)^2
=Y(X^2-7X+6)

解：x^4+x^2y^2+y^4
=x^4+2x^2y^2+y^4 -x^2y^2
=（x^2+y^2）^2-x^2y^2
=(x^2+y^2+xy)(x^2+y^2-xy)

x^2y-7xy+6y
=y(x^2-7x+6 )
=y(x-1)(x-6)

x^4+x^2y^2+y^4
=x^4+2x^2y^2+y^4-x^2y^2
=(x^2+y^2)^2-x^2y^2
下面用平方差公式
=(x^2+y^2+xy)(x^2+y^2-xy)

x^2y-7xy+6y
=x^2y-xy-6xy+6y
=xy(x-1)-6y(x-1)
=(xy-6y)(x-1)
=y(x-6)(x-1)