因式分解x4+y4+z4-2x2y2-2x2z2-2y2z2
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/22 13:22:26
因式分解x4+y4+z4-2x2y2-2x2z2-2y2z2
x,y,后的2为平方.
x,y,后的2为平方.
x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2
=x^4-2x^2y^2+y^4+z^4-2x^2z^2-2y^2z^2
=(x^4-2x^2y^2+y^4)+(z^4-2x^2z^2-2y^2z^2)
=(x^2-y^2)^2+z^4-2y^2z^2+2z^2x^2-4z^2x^2
=(x^2-y^2)^2+2z^2(x^2-y^2)+z^4-4z^2x^2
=(x^2-y^2+z^2)^2-4z^2x^2
=(x^2-y^2+z^2+2zx)(x^2-y^2+z^2-2zx)
=[(x+z)^2-y^2][(x-z)^2-y^2]
=(x+y+z)(x-y+z)(x+y-z)(x-y-z)
=x^4-2x^2y^2+y^4+z^4-2x^2z^2-2y^2z^2
=(x^4-2x^2y^2+y^4)+(z^4-2x^2z^2-2y^2z^2)
=(x^2-y^2)^2+z^4-2y^2z^2+2z^2x^2-4z^2x^2
=(x^2-y^2)^2+2z^2(x^2-y^2)+z^4-4z^2x^2
=(x^2-y^2+z^2)^2-4z^2x^2
=(x^2-y^2+z^2+2zx)(x^2-y^2+z^2-2zx)
=[(x+z)^2-y^2][(x-z)^2-y^2]
=(x+y+z)(x-y+z)(x+y-z)(x-y-z)
已知x+y+z=0,求x4+y4+z4-2x2y-2y2z2-2z2x2的值
因式分解:x4次方-2x²y²+y4次方
已知x+y+z=1 x2+y2+z2=2 x3+y3+z3=3 求x4+y4+z4=?
若x+y=1则代数式x4+6x3y—2x2y+10x2y2—2xy2+6xy3+y4的值等于_____
已知x2+4y2+x2y2-6xy+1=0,求 x4-y4/2x-y 乘 2xy-y2/xy-y2 除以(x2+y2/x
因式分解 x5n+xn+1 2a2-a2b+(b-2)(ab-a)2 x5+x4+x3+x2+x+1 x4+y4-2x2
计算(1)(a-b+c-d)(c-a-d-b);(2)(x+2y)(x-2y)(x4-8x2y2+16y4).
分解因式:16x4-72x2y2+81y4.
有这样一道题,计算(2x4-4x3y-x2y2)-2(x4-2x3y-y3)+x2y2的值,其中x=0.25,y=-1;
已知:x2+y2=4xy,求(x4+y4)÷(xy)2
因式分解:x4+x2-2ax-a2+1
数学因式分解跟计算题x2-4(x-1) x4-y4 (5a2次方+2a)—4(2+2a次方) 4(x-y)3次方乘{-2