A) x(x+4)(x-4)-(x^2+1)(x^2-1)
= x(x^2 - 16) - x^4 + 1
= x^3 - 16x - x^4 + 1
B) (y-3)(y+3)(y^2+9)-(y^2+2)(y^2-2)
= (y^2 - 9)(y^2 + 9) - y^4 + 4
= y^4 - 81 - y^4 + 4
= -77
C) (a+b-c)^2-(a-c)^2-2ab+2bc
= a^2 + b^2 - c^2 + 2ab - 2ac - 2bc - a^2 + 2ac - c^2 - 2ab + 2bc
= - 2c^2 + b^2

Bài 1:
a) x(x + 4)(x - 4) - (x^2 + 1)(x^2 - 1)
= x(x^2 - 16) - x^4 + 1
= x^3 - 16x - x^4 + 1
b) (y - 3)(y + 3)(y^2 + 9) - (y^2 + 2)(y^2 - 2)
= (y^2 - 9)(y^2 + 9) - y^4 + 4
= y^4 - 81 - y^4 + 4
= -77
c) (a+b-c)^2-(a-c)^2-2ab+2bc
=a^2+b^2- c^2+2ab - 2ac-2bc -a^2+2ac- c^2-2ab +2bc
= - 2c^2 + b^2

Bài 2:
a, Ta có:
(a + b)^2 = a^2 + 2ab + b^2
                 = a^2 - 2ab + b^2 + 2ab + 2ab
                 = (a - b)^2 + 4ab => đpcm
Vậy . . .
b, Ta có:
(a - b)^2 = a^2 - 2ab + b^2
               = a^2 + 2ab + b^2 - 2ab - 2ab
                = (a + b)^2 - 4ab => đpcm
Vậy . . .
c, Ta có:
(a^2 - b^2)^2 + (2ab)^2
= a^4 - 2a^2.b^2 + b^4 + 4a^2.b^2
= a^4 + 2a^2.b^2 + b^4 = (a^2 + b^2)^2 => dpcm
Vậy. . .