Question

Bài tập 1 : Rút gọn các biểu thức sau :

\(A=100^2-99^2+98^2-97^2+...+2^2-1^2\) \(B=3.\left(2^2+1\right)\left(2^4+1\right)....\left(2^{64}+1\right)+1\)

\(C=\left(a+b+c\right)^2+\left(a+b-c\right)-2.\left(a+b\right)^2\)

Answer 1

A = 100² - 99² + 98² - 97² + . . . + 2² - 1²

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

= 199 + 195 + . . . + 3

= 5050

B = 3(2² + 1)(2⁴ + 1) . . . (2⁶⁴ + 1) + 1

= (2² - 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1)(2⁶⁴ + 1)(2⁶⁴ + 1) + 1

= (2⁴ - 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1)(2⁶⁴ + 1) + 1

= (2⁸ - 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1)(2⁶⁴ + 1) + 1

= (2¹⁶ - 1)(2¹⁶ + 1)(2³² + 1)(2⁶⁴ + 1) + 1

= (2³² - 1)(2³² + 1)(2⁶⁴ + 1) + 1

= (2⁶⁴ - 1)(2⁶⁴ + 1) + 1

= 2¹²⁸ - 1 + 1

= 2¹²⁸

Answer 2

Câu C mk chép nhầm đề đó