Bài `14:`
`a)`
`81^2 = (80+1)^2 = 80^2 + 2 . 80 . 1 + 1^2 = 6400 + 160 + 1 = 6561`
`b)`
`102^2 = (100+2)^2 = 100^2 + 2 . 100 . 2 +2^2 = 10000 + 400 + 4 = 10404`
`c)`
`97 . 103 = (100-3)(100+3) = 100^2 - 3^2 = 10000 - 9 = 9991`
`d)`
`249 . 351 = (300 - 51)(300+51) = 300^2 - 51^2 = 90000 - 2601 = 87399`
Bài `15:`
`a)`
`A = (5x+5)^2 + 10(x-3)(1+x) + x^2 - 6x + 9`
` = [(5x)^2 + 2 . 5x . 5 + 5^2] + (10x -30)(x+1) + x^2 - 6x + 9`
` = 25x^2 + 50x + 25 + 10x^2 + 10x - 30x - 30 + x^2 - 6x +9`
` = (25x^2 + 10x^2 + x^2) + (50x + 10x - 30x - 6x) + (25 -30+9)`
` = 36x^2 + 24x + 4`
Vậy `A = 36x^2 + 24x + 4`
`b)`
`B = (x-1)^2/4 + x^2 - 1 + (x+1)^2`
`= (x^2- 2x+1)/4 + x^2 - 1 + x^2 + 2x + 1`
` = (x^2- 2x + 1)/4 + 2x^2 + 2x`
` = (x^2 -2x+1)/4 + (8x^2 +8x)/4`
` = (x^2 - 2x+1 + 8x^2 + 8x)/4`
` = (9x^2 + 6x+1)/4`
Vậy `B = (9x^2 + 6x+1)/4`
