lam hộ em ạ thankssssss

Bài `3:`

`a) 7x^2 - 7xy - 4x + 4y`

` = 7x . (x - y) - 4 . (x-y)`

` = (7x - 4) . (x-y)`

`b) x^2 - 2x - 4y^2 -4y`

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

` = (x^2 - 2 . x . 1  +1^2) -[ (2y)^2 - 2 . 2y . 1 + 1^2]`

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

` = [ (x-1) + (2y-1) ] . [ (x-1) - (2y - 1) ]`

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

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

`c) x^3 + 10x^2 +  25x - xy^2`

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

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

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

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

`d) 2x - 2y - x^2 + y^2`

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

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

` = (x-y) . [ 2 - (x+y) ] `

`  = (x-y) . (2 - x - y)`

`e) x^3 - 4x^2 + 12x - 27`

` = x^3 - x^2 - 3x^2 + 9x + 3x  - 27`

`  = (x^3 - x^2 + 9x ) - (3x^2 - 3x + 27)`

` = x . (x^2 - x + 9 ) - 3 . (x^2 - x + 9)`

` = (x-3) . (x^2 - x + 9 )`

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

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

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

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

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

`g) x^2 + x - 6`

` = x^2 - 2x + 3x - 6`

` = x . (x-2)  + 3 . (x-2)`

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

`h) x^3 - x^2 - 4x^2 + 8x - 4`

` = x^3 - x^2 - 4x^2 + 4x + 4x - 4`

` = x^2 . (x-1) - 4x . (x-1) + 4 . (x-1)`

` = (x^2 - 4x + 4) . (x-1)`

` = (x^2 - 2 . x . 2 + 2^2) . (x-1)`

` = (x-2)^2 . (x-1)`

`i) 2x^2 + 4x - 30`

` = 2x^2 - 6x + 10x - 30`

` = 2x . (x-3) + 10 . (x-3)`

` = (2x + 10 ) . (x-3)`

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

Bài `4:`

`a) x^3 - 64x = 0 `

`<=> x. (x^2 - 64) = 0`

`<=> x = 0` hoặc `x^2 - 64=0`

`+)x=0`

`+)x^2 - 64 = 0`

`<=> x^2 = 64`

`<=> x = 8` hoặc `x = -8`

Vậy `x \in { 0 ; 8 ; -8 }`

`b) x^3- 6x^2 + 12x - 8 = 0 `

`<=> x^3 - 3 . x^2 . 2 + 3 . x . 2^2 - 2^3 = 0`

`<=> (x-2)^3 = 0`

`<=> x - 2 = 0`

`<=> x = 2`

Vậy `x = 2`

`c) x^2 - 16 - (x-4) = 0`

`<=> (x-4) . (x+4) - (x-4) = 0`

`<=> (x-4) . (x+4 - 1)=0`

`<=> (x-4) . (x+3) = 0`

`<=> x-4=0` hoặc `x+3=0`

`+)x-4=0<=>x=4`

`+)x+3=0<=> x=-3`

Vậy `x \in { 4  ; -3}`

`d) 6x . (x-5)  = (x-5)`

`<=> 6x . (x-5) - (x-5) = 0`

`<=> (6x-1).(x-5) = 0`

`<=> 6x - 1 = 0` hoặc `x-5=0`

`+)6x - 1  =0 <=> 6x = 1 <=> x = 1/6`

`+)x-5=0<=>x=5`

Vậy `x \in{ 1/6 ; 5}`

`e) x^3 - 7x - 6 = 0`

`<=> x^3 - 3x^2 + 3x^2 - 9x + 2x - 6 = 0`

`<=> x^2 . (x-3) + 3x . (x-3) + 2 . (x-3) = 0`

`<=> (x^2 + 3x + 2) . (x-3) = 0`

`<=> (x^2 + 2x + x + 2) . (x-3)=0`

`<=> [x.(x+2) + (x+2) ]  . (x-3) =0`

`<=> (x+1).(x+2).(x-3)=0`

`+) x + 1= 0 <=> x = -1`

`+) x + 2 = 0 <=> x = -2`

`+) x - 3 = 0 <=> x =3`

Vậy `x \in { -1 ; -2 ; 3 }`

`f) x^3 - 4x^2  = - 4x `

`<=> x^3 - 4x^2 + 4x = 0`

`<=> x. (x^2 - 4x + 4) = 0`

`<=> x. (x^2 - 2 . x . 2 + 2^2) = 0`

`<=> x . (x-2)^2 = 0`

`<=> x= 0` hoặc `(x-2)^2 = 0`

`+)x=0`

`+)(x-2)^2 = 0 <=> x- 2 = 0 <=> x =2`

Vậy `x \in { 0 ; 2 } `

`g) (2x+1)^2 = (3+x)^2`

`<=> (2x+1)^2 - (3+x)^2 = 0`

`<=> [ (2x+1) - (3+x) ] . [ (2x+1) + (3 + x) ] = 0`

`<=> (2x + 1 - 3 - x) . (2x + 1+3 + x) = 0`

`<=> (x -2) . (3x + 4) =0`

`<=> x -2 = 0` hoặc `3x +4=0`

`+)x-2=0<=>x=2`

`+)3x+4=0<=> 3x = -4 <=> x = -4/3`

Vậy `x \in {2 ; -4/3}`

`h) x^2 + y^2 - 6x + 6y + 18 = 0`

`<=> (x^2 - 6x + 9) + (y^2 + 6y + 9) = 0`

`<=> (x^2 - 2 . x . 3 + 3^2) + (y^2 + 2 . x . 3 + 3^2) = 0`

`<=> (x-3)^2 + (y + 3)^2 = 0`

`\forall x` ta có :

`(x-3)^2 \ge 0`

`(y+3)^2 \ge 0`

`=> (x-3)^2 + (y+3)^2 \ge 0`

Dấu `=` xảy ra 

`<=>`$\begin{cases}   x- 3 = 0 \\   y + 3 = 0 \end{cases}$

`<=>` $\begin{cases}
  x = 3  \\
  y = -3
\end{cases}$

Vậy $\begin{cases}
  x = 3  \\
  y = -3
\end{cases}$