Rút gọn biểu thức:
a) (x2 - 2x +2)(x2 - 2)(x2 + 2x +2)(x2 + 2)
b) (x + 1)3 + (x - 1)3 + x3 - 3x(x + 1)(x - 1)
c) (a + b + c)2 + (a + b - c)2 + (2a - b)2
d) 1002 - 992 + 982 - 872 + ... + 22 - 1
e) 3(22 + 1)(24 + 1)(25 + 1) ... (264 + 1) +1
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b) \(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)
\(=3x^3+6x-3x^3+3x\)
\(=3x\)
d) \(100^2-99^2+98^2-97^2+...+2^2-1\)
\(=\left(100+99\right)\left(100-99\right)+\left(98+97\right)\left(98-97\right)+..+\left(2+1\right)\left(2-1\right)\)
\(=100+99+98+97+..+2+1\)
\(=\frac{\left(100+1\right)\cdot100}{2}=5050\)