高一数学计算题
（1）计算(x-1)(x-2)(x-3)(x-4)（2）计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)...
（1）计算(x-1)(x-2)(x-3)(x-4)
（2）计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z) 展开
（2）计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z) 展开
3个回答
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1.(X-1)(X-2)(X-3)(X-4)
=(X-1)(X-4) (X-2)(X-3)
=（x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24
2.原式=[(y+z)+x][(y+z)-x][x-(y-z)][x+(y-z)]
=[(y+z)²-x²][x²-(y-z)²]
=(y²+2yz+z²-x²)(x²-y²-z²+2yz)
=[2yz+(y²+z²-x²)][2yz-(y²+z²-x²)]
=(2yz)²-(y²+z²-x²)²
=-x²-y²-z²+2x²y²+2y²z²+2y²z²
=(X-1)(X-4) (X-2)(X-3)
=（x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24
2.原式=[(y+z)+x][(y+z)-x][x-(y-z)][x+(y-z)]
=[(y+z)²-x²][x²-(y-z)²]
=(y²+2yz+z²-x²)(x²-y²-z²+2yz)
=[2yz+(y²+z²-x²)][2yz-(y²+z²-x²)]
=(2yz)²-(y²+z²-x²)²
=-x²-y²-z²+2x²y²+2y²z²+2y²z²
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展开全部
1. =(x^2-5x+4)(x^2-5x+6)=(x^2-5x)^2+10(x^2-5x)+24=x^4-10x^3+35x^2-50x+24
2. =[(x+y)^2-z^2][(x-y)^2-z^2]=z^4-(2x^2+2y^2)+(x^2-y^2)^2=x^4+y^4+z^4-2(x^2+y^2+z^2)
2. =[(x+y)^2-z^2][(x-y)^2-z^2]=z^4-(2x^2+2y^2)+(x^2-y^2)^2=x^4+y^4+z^4-2(x^2+y^2+z^2)
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