Question

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

Các bạn giúp mình với!!! Mình đang rất rất cần

Answer 1

b) \(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)

\(=3x^3+6x-3x^3+3x\)

\(=3x\)

Answer 2

d) \(100^2-99^2+98^2-97^2+...+2^2-1\)

\(=\left(100+99\right)\left(100-99\right)+\left(98+97\right)\left(98-97\right)+..+\left(2+1\right)\left(2-1\right)\)

\(=100+99+98+97+..+2+1\)

\(=\frac{\left(100+1\right)\cdot100}{2}=5050\)