x3次方(y-z) y3次方(z-x) z3次方(x-y)
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a^3+b^3=(a+b)(a^2-ab+b^2)a^3-b^3=(a-b)(a^2+ab+b^2)(x+y+z)^3-x^3-y^3-z^3=(y+z)[(x+y+z)^2+(x+y+z)x+x^2
∵x+y+z=0,∴z=(-x-y)x^3+y^3+z^3=x^3+y^3-(x+y)^3=x^3+y^3-x^3-y^3-3x^2y-3xy^2=-3xy(x+y)=3xyz
x^3+y^3-x^2y-xy^2=x^2(x-y)-y^2(x-y)=(x^2-y^2)(x-y)=(x+y)(x-y)^2,因为x+y大于0,(x-y)^2大于等于0,所以x^3+y^3大于等于x
∵(x+y+z)(x²+y²+z²)=x³+y³+z³+x²(y+z)+y²(x+z)+z²(x+y)∴1*2
证明:因为x2+y2≥2xy≥0(2分)所以x3+y3=(x+y)(x2-xy+y2)≥xy(x+y)(4分)同理y3+z3≥yz(y+z),z3+x3≥zx(z+x)(8分)三式相加即可得2(x3+
(x+y+z)^3-x^3-y^3-z^3=3yx^2+3xy^2+3xz^2+3yz^2+3zx^2+3zy^2+6xyz=3xy(x+y)+3z^2(x+y)+3z(x^2+y^2+2xy)=3x
如果你的X2是x的平方,X3是x的三次方那么答案是:-(x-y+z)*(x-y-z)*(x+y-z)
要求的式子=(x³-y³)+(3xy²-x²y)-2(x²y-y³)=x³-y³+3xy²-x²y-
^3代表3次方,^2代表平方X^3+X^2-Y^3-Y^2=(x^3-y^3)+(x^2-y^2)=(x-y)(x^2+xy+y^2)+(x-y)(x+y)=(x-y)(x^2+xy+y^2+x+y)
√32x3次方y平方z=4lxyl√2xz
x3(y-z)+y3(z-x)+z3(x-y)=x3(y-z)+y3(z-x)-z3(y-z)-z3(z-x)=(x3-z3)(y-z)+(y3-z3)(z-x)=(x-z)(y-z)(x2+xz+z
这是要立方和公式,x^3+y^3+3xy=(x+y)(x^2-xy+y^2)+3xy=x^2-xy+y^2+3xy=(x+y)^2=1
x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2=(x^4+y^4-2x^2y^2)+z^4-2x^2z^2-2y^2z^2=(x^2-y^2)^2-2(x^2-y^2)z^2+
题目是否有误?原式左边化简后等于:=(x-y)^3,再表达成=x^3+(),意义不大吧x^3-3x^2y+3xy^2-y^3=x^3+(3xy^2-3x^2y-y^3)
x^3+y^3+z^3+(x+y)^3+(y+z)^3+(z+x)^3=[x^3+(y+z)^3]+[y^3+(z+x)^3]+[z^3+(x+y)^3]=(x+y+z)(x^2-xy+y^2-xz+
因为x^3+y^3+z^3-3xyz=(x+y)^3-3x^y-3xy^2+z^3-3xyz(把x^3+y^3写成(x+y)^3-3x^2y-3xy^2)=[(x+y)^3+z^3]-(3x^2y+3
x3次方-xy平方+x平方y-y3次方=x(x²-y²)+y(x²-y²)=(x+y)(x²-y²)=(x+y)(x+y)(x-y)=(x+
X^2+y^2=(x+y)^2-2Xy=a^2-2bx3次方+y3次方=(x+y)(X^2+y^2-xy)=a(a^2-2b-b)=a^3-3abx4次方+y4次方=(x^2+y^2)^2-2x^2y