Question

[Vũ Hà My]

Rút gọn biểu thức:

a) \(\left(x^2-2x+2\right)\left(x^2-2\right)\left(x^2+2x+2\right)\left(x^2+2\right)\)

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

c) \(100^2-99^2+98^2-97^2+...+2^2-1^2\)

d) \(3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

Giup mình vs mình dang cần gấp

Answer 1

[Thi Chinh Dinh]

a) ( x² - 2x + 2 )( x² - 2 )( x² + 2x + 2 )( x² + 2 )

= [ ( x² + 2 )² - 4x² ] ( x⁴ - 4 )

= ( x⁴ + 4 ) ( x⁴ - 4 )

= x⁸ - 16

b) ( a + b + c )² + ( a + b - c )² + ( 2a -b )²

= 2 ( a² + b² + c² ) + 2 ( ab + bc + ac ) + 2 ( ab - bc - ac ) + ( 4a² - 4ab + b² )

= 2 ( a² + b² + c² ) + 4ab - 4ab + 4a² + b²

= 6a² + 3b² + 2c²

c) 100² - 99² + 98² - 97² + ..... + 2² - 1²

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

= 199 + 197 + 195 + ..... + 5 + 3

= \(\frac{\left(199+3\right)\left(\left(199-3\right)\frac{1}{2}+1\right)}{2}\)

= 9999

d) 3 ( 2² + 1 )( 2⁴ +1 )......( 2⁶⁴ + 1 ) + 1

= ( 2² -1 )( 2² + 1 )(2⁴ + 1 ).....( 2⁶⁴ + 1 ) + 1

= ( 2⁴ -1 )( 2⁴ + 1 )( 2⁸ + 1 )......( 2⁶⁴ + 1 ) +1

= ( 2⁸ -1 )( 2⁸ + 1).....( 2⁶⁴ + 1) +1

............

= ( 2⁶⁴ - 1)( 2⁶⁴ +1 ) + 1

= 2¹²⁸