Đáp án`+`Giải thích các bước giải:

 `1, x^2 + 9 - 16y^2 + 6x`

`= (x^2 + 6x + 9) - 16y^2`

`= (x + 3)^2 - (4y)^2`

`= (x + 3 - 4y)(x + 3 + 4y)`

`2, x^2 - 9 + y^2 + 2xy`

`= (x^2 + 2xy + y^2) - 9`

`= (x +y)^2 - 3^2`

`= (x + y - 3)(x + y + 3)`

`3, x^2 - 4x + 4 - 9y^2`

`= (x - 2)^2 - (3y)^2`

`= (x - 2 - 3y)(x - 2 + 3y)`

`4, x^2 - 4xy + 4y^2 - 81`

`= (x - 2y)^2 - 9^2`

`= (x - 2y - 9)(x - 2y + 9)`

`5, 25 - 10x - 9y^2 +x^2`

`= (x^2 - 10x + 25) - 9y^2`

`= (x - 5)^2 - (3y)^2`

`= (x - 5 -3y)(x - 5 + 3y)`

`6, 9y^2 - 4x^2 + 4x - 1`

`= 9y^2 - (4x^2 - 4x + 1)`

`= (3y)^2 - (2x - 1)^2`

`= (3y - 2x + 1)(3y + 2x - 1)`

`7, x^2 - 2x - 4y^2 + 4y`

`= (x^2 - 4y^2) - (2x -4y)`

`= (x - 2y)(x + 2y) - 2(x - 2y)`

`= (x - 2y)(x + 2y - 2)`

`8, 64 -4x^2 + 12xy - 9y^2`

`= 8^2 - (2x - 3y)^2`

`= (8 - 2x + 3y)(8 + 2x - 3y)`

`9, 6x^2 + 6y^2 - 24 + 12xy`

`= 6[(x^2 + 2xy + y^2) - 4]`

`= 6[(x + y)^2 - 2^2]`

`= 6(x + y - 2)(x+ y +2)`

`10, 9x^2 - 6x + 1 - 25`

`= (3x - 1)^2 - 5^2`

`= (3x - 1 -5)(3x - 1+ 5)`

`= (3x- 6)(3x + 4)`

`= 3(x - 2)(3x + 4)`

`11, x^2 + 4x + 4-  49y^2`

`= (x + 2)^2 - (7y)^2`

`= (x + 2 - 7y)(x + 2 + 7y)`

`12, a^3 + 9a - ab^2 - 6a^2`

`= a(a^2 + 9 - b^2 - 6a)`

`= a[(a - 3)^2 - b^2]`

`= a(a - 3 -b)(a - 3 + b)`

`13, 9x^2 + 6x +1 - 25`

`= (3x + 1)^2 - 5^2`

`= (3x + 1 - 5)(3x + 1+ 5)`

`= 3(3x - 4)(x + 2)`

`24, a^2 + 6a - 4b^2 + 9`

`= (a + 3)^2 - (2b)^2`

`= (a + 3 - 2b)(a + 3 + 2b)`

`14, 5x^2 - 10x + 5 - 45t^2`

`= 5(x^2 - 2x + 1 - 9t^2)`

`= 5[(x - 1)^2- (3t)^2]`

`= 5(x - 1 - 3t)(x - 1 + 3t)`

`15, x^2 - 36y^2 t^2 - 10x + 25`

`= (x - 5)^2 - (6yt)^2`

`= (x - 5 - 6yt)(x - 5 + 6yt)`

`***`sharksosad