Đáp án:
$a) (x^2-1)^3 - (x^4+x^2+1)(x^2-1)$
$ = x^6 -3.x^4 +3x^2 -1 - (x^6 -x^4 +x^4 -x^2+x^2-1)$
$ = x^6 -3x^4 +3x^2 -1 -x^6 +x^4 -x^4 +x^2 -x^2 +1$
$ = x^6 -x^6 -3x^4 -x^4+x^4 +3x^2+x^2-x^2 -1+1$
$ = -3x^4+3x^2$
$b) (x^4-3x^2 +9)(x^2 +3) - (3+x^2)^3$
$ = x^6 +3x^4 -3x^4 -9x^2+9x^2 +27 - (27+27x+9x^4+x^6)$
$ = x^6 +27 - 27 -27x-9x^4 -x^6$
$ = -9x^4 -27x$
$c) 4(x+1)^4 +(2x-1)^2-8(x-1)(x+1)$
$ = 4(x+1)^2.(x+1)^2 + (2x-1)^2 -8(x-1)(x+1)$
$ = 4(x^2+2x+1)(x^2+2x+1) + (4x^2-4x+1) -8x^2-8x+8x+8$
$ = 4(x^4 +2x^3+x^2+2x^3+4x^2+2x+x^2+2x+1) + 4x^2-4x+1 -8x^2 +8$
$ = 4(x^4 +4x^3+6x^2 + 4x+1) -4x^2-4x+9$
$ =4x^4 +16x^3 +24x^2+16x+4 -4x^2-4x+9$
$ = 4x^2+16x^3 +20x^2 +12x +13$
$d) (a+b-c)^2 -(a+b)^2 + 2c(a+b)$
$ = a^2+b^2+c^2+2ab-2ac-2bc - (a^2+2ab+b^2) +2ac+2bc$
$ =a^2+b^2+c^2+2ab-2ac-2bc -a^2-2ab-b^2 +2ac+2bc$
$ = a^2 -a^2 +b^2-b^2 +c^2 +2ab-2ab -2ac+2ac-2bc+2bc$
$ =c^2$
