Giải thích các bước giải:
34/.
$(x^2+y^2)^3+(z^2-x^2)^3-(y^2+z^2)^3$
$=x^6+3x^4y^2+3x^2y^4+y^6+z^6-3z^4x^2+3z^2x^4-x^6-(y^6+3y^4z^2+3y^2z^4+z^6)$
$=x^6+3x^4y^2+3x^2y^4+y^6+z^6-3z^4x^2+3z^2x^4-x^6-y^6-3y^4z^2-3y^2z^4-z^6$
$=(x^6-x^6)+3x^4y^2+3x^2y^4+(y^6-y^6)+(z^6-z^6)-3z^4x^2+3z^2x^4-3y^4z^2-3y^2z^4$
$=3x^4y^2+3x^2y^4-3z^4x^2+3z^2x^4-3y^4z^2-3y^2z^4$
$=3(x^4y^2+x^2y^4-z^4x^2+z^2x^4-y^4z^2-y^2z^4)$
$=3(x^4y^2+x^2y^4-z^4x^2+z^2x^4-y^4z^2-y^2z^4)$
$=3(x^4y^2+x^2y^4+x^2y^2z^2-x^2y^2z^2-x^2z^4+x^4z^2-y^4z^2-y^2z^4)$
$=3[(x^4y^2+x^4z^2-x^2y^2z^2-x^2z^4)+(x^2y^4+x^2y^2z^2-y^4z^2-y^2z^4)]$
$=3[x^2(x^2y^2+x^2z^2-y^2z^2-z^4)+y^2(x^2y^2+x^2z^2-y^2z^2-z^4)]$
$=3(x^2y^2+x^2z^2-y^2z^2-z^4)(x^2+y^2)$
$=3[x^2(y^2+z^2)-z^2(y^2+z^2)(x^2+y^2)]$
$=3[(y^2+z^2)(x^2-z^2)(x^2+y^2)]$
$=3[(y^2+z^2)(x^2-z^2)(x^2+y^2)]$
$=3[(y^2+z^2)(x-z)(x+z)(x^2+y^2)]$
(Mình tự làm, không copy bạn nhé)
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