[TOÁN 8] chia đa thức cho đơn thức !cần gấp

T

transformers123

$A=(a+b-c)^3+(a-b+c)^3+(-a+b+c)^3-(a+b+c)^3$

Đặt $a+b-c=x,\ a-b+c=y,\ -a+b+c=z,$ ta có:

$A=x^3+y^3+z^3-(x+y+z)^3$

$\iff A=x^3+y^3+z^3-[x^3+y^3+z^3+3(x+y)(y+z)(z+x)]$

$\iff A=-3(x+y)(y+z)(z+x)$

$\iff A=-3(a+b-c+a-b+c)(a-b+c-a+b+c)(-a+b+c+a+b-c)$

$\iff A=-24abc$

Vậy $A:(24abc)=-1#
 
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