Đáp án:
Giải thích các bước giải:
$a)(x-1)^3-(x+1)^3+6(x-1)(x+1)_{}$
$⇔x^3-3x^2+3x-1-(x^3+3x^2+3x+1)+6(x^2-1)_{}$
$⇔x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x^2-6_{}$
$⇔-8_{}$
$c)(x-2)^2-(x-3)(x-1)_{}$
$⇔x^2-4x+4-(x^2-x-3x+3)_{}$
$⇔x^2-4x+4-(x^2-4x+3)_{}$
$⇔x^2-4x+4-x^2+4x-3_{}$
$⇔1_{}$
$Bài5:_{}$
$b)a^2+b^2-c^2-d^2-2ab+2cd_{}$
$⇔(a-b)^2-(c^2-2cd+d^2)_{}$
$⇔(a-b)^2-(c-d)^2_{}$
$⇔[ a-b-(c-d)].[ a-b+(c-d)]_{}$
$⇔(a-b-c+d).(a-b+c-d)_{}$
$d)x^2(y-z)+y^2(z-x)+z^2(x-y)_{}$
$⇔x^2y-x^2z+y^2z-xy^2+xz^2-yz^2_{}$
$f)x^{12}-3x^6y^6+2y^{12}_{}$
$⇔x^{12}-x^6y^6-2x^6y^6+2^{12}_{}$
$⇔x^6.(x^6-y^6)-2y^6.(x^6-y^6)_{}$
$⇔(x^6-y^6)(x^6-2y^6)_{}$
$⇔(x^3-y^3)(x^3+y^3)(x^6-2y^6)_{}$
$⇔(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)(x^6-2y^6)_{}$
$h)(x^2-8)^2-784_{}$
$⇔(x^2-8-28)(x^2-8+28)_{}$
$⇔(x^2-36)(x^2+20)_{}$
$⇔(x-6)(x+6)(x^2+20)_{}$
