Đáp án:

1. Ta có :

`x^2 - 6x - y^2 + 9`

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

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

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

2. Ta có : 

`25 - 4x^2 - 4xy - y^2`

` = 25 - (4x^2 + 4xy + y^2)`

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

` = (5 + 2x + y)(5 - 2x - y)`

3, Ta có : 

`9(x + 5)^2 - (x - 7)^2`

` = 3^2.(x + 5)^2 - (x - 7)^2`

` = [3.(x + 5)]^2 - (x - 7)^2`

` = (3x + 15)^2 - (x - 7)^2`

` = (3x + 15 - x + 7)(3x + 15 + x - 7)`

` = (2x + 22)(4x + 8)`

` = 2.(x + 11).4.(x + 2)`

` = 9(x + 11)(x + 2)`

4. Ta có : 

`a^2 - ab - b + a`

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

` = a.(a + 1) - b.(a + 1)`

` = (a - b)(a + 1)`

5. Ta có : 

`ac - bc - 5(b - a)`

` = c.(a - b) + 5.(a - b)`

` = (c + 5)(a - b)`

6. Ta có : 

`a^3 - a^2x - ay^2 + xy^2`

` = (a^3 - a^2x) - (ay^2 - xy^2)`

` = a^2.(a - x) - y^2.(a - x)`

` = (a^2 - y^2).(a - x)`

` = (a  - y)(a + y)(a - x)`

7. Ta có  :

`x^2 + 2xy + y^2 - xz - yz`

` = (x^2 + 2xy + y^2) - (xz + yz)`

` = (x + y)^2 - z.(x + y)`

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

8. Ta có : 

`x^2 - 4xy + 4y^2 - z^2 + 4zt - 4t^2`

` = (x^2 - 4xy + 4y^2) - (z^2 - 4zt + 4t^2)`

` = (x - 2y)^2 - (z - 2t)^2`

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

Giải thích các bước giải:

 

1) $(x^2-6x+9)-y^2$

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

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

2) $25-4x^2-4xy-y^2$

$=5^2-(4x^2+4xy+y^2)$

$=5^2-(2x+y)^2$

$=(5-2x-y)(5+2x+y)$

3) $9(x+5)^2-(x-7)^2$

$=(3x+15)^2-(x-7)^2$

$=(3x+15+x-7)(3x+15+7-x)$

$=(4x+8)(2x+22)$

$=8(x+2)(x+11)$

4) $a^2-ab-b+a$

$=a(a-b)+(a-b)$

$=(a-b)(a+1)$

5) $ac-bc-5(b-a)$

$=c(a-b)+5(a-b)$

$=(a-b)(c+5)$

6) $a^2(a-x)-y^2(a-x)$

$=(a-x)(a^2-y^2)$

$=(a-x)(a-y)(a+y)$

7) $x^2+2xy+y^2-xz-yz$

$=(x+y)^2-z(x+y)$

$=(x+y)(x+y-z)$

8) $(x-2y)^2-(z-2t)^2$

$=(x-2y+z-2t)(x-2y+2t-z)$