Đáp án:
Bài `1`
`a, (9x^2 + 1)^2 - 36x^2`
`= (9x^2 + 1)^2 - (6x)^2`
`= (9x^2 + 1 + 6x)(9x^2 + 1 - 6x)`
`= [(3x)^2 + 2.x.1 + 1^2][(3x)^2 - 2.3x.1 + 1^2]`
`= (3x + 1)^2 (3x - 1)^2`
`b, 9x^2 + 6xy - 8y^2`
`= 9x^2 + 6xy + y^2 - 9y^2`
`= [(3x)^2 + 2.3x.y + y^2] - 9y^2`
`= (3x + y)^2 - (3y)^2`
`= (3x + 3y + y)(3x + y - 3y)`
`= (3x + 4y)(3x - 2y)`
`c, x^3 - 9x^2 + 27x - 27`
`= x^3 - 3.x^2 .3 + 3.x.3^2 - 3^3`
`= (x - 3)^3`
`d, 2x^3 - 9x^2 + 27x - 27`
`= x^3 + (x^3 - 9x^2 + 27x - 27)`
`= x^3 + (x - 3)^2`
`= (x + x - 3)[x^2 - x(x - 3) + (x - 3)^2]`
`= (2x - 3)(x^2 - x^2 + 3x + x^2 - 6x + 9)`
`= (2x - 3)(x^2 - 3x + 9)`
Bài `2`:
`a, A = 9 - (2 + 5n)^2`
`= 9 - [2^2 + 2.2.5n + (5n)^2]`
`= 9 - (4 + 20n + 25n^2)`
`= 9 - 4 - 20n - 25n^2`
`= 5 - 20n - 25n^2`
`= 5(1 - 4n - 5n^2)`$\vdots$ `5`
`→ đpcm`
Vậy `A = 9 - (2 + 5n)^2` $\vdots$ `5`
`b, B = (2n - 3)^2 - 25`
`=(2n)^2 - 2.2n.3 + 3^2 - 25`
`= 4n^2 - 12n + 9 - 25`
`= 4n^2 - 12n - 16`
`→` Thiếu đề
