`a)`
`100^2 - 99^2 + 98^2 - 97^2 + ... + 2^2 -1`
`= \underbrace{(100^2 - 99^2) + (98^2- 97^2) + ... + (2^2-1) }_{\text{có 50 nhóm}}`
`= \underbrace{ [(100-99)(100+99)] + [(98 - 97)(98+97)] + ... + [(2-1)(2+1)] }_{\text{có 50 nhóm}}`
`= 100 + 99 + 98 + 97 + .... + 2 + 1 `
`= \underbrace{(100+1) + (99+2) + (98+3).. + (50+51) }_{\text{có 50 nhóm}}`
` = \underbrace{101 + 101 + 101 + ... + 101 }_{\text{có 50 số hạng}}`
` = 50 . 101`
` = 5050`
`b)`
`48 (5^2 + 1)(5^4+1)(5^8+1)(5^16+1)(5^32+1)`
`= 2 (5^2 - 1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)(5^32+1)`
`= 2 (5^4-1)(5^4+1)(5^8+1)(5^16+1)(5^32+1)`
`= 2 (5^8-1)(5^8+1)(5^16+1)(5^32+1)`
`= 2 (5^16 -1)(5^16+1)(5^32+1)`
`= 2 (5^32 - 1)(5^32+1)`
`= 2 (5^64 -1)`
