Đáp án:

Giải thích các bước giải:

Bài 1: Tính

a) 2x ( - 3x + 5 )

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

= - 6x² + 10x

b) ( 5x - 3 )( 1 - 2x )

= 5x . 1 + 5x . ( - 2x ) - 3 . 1 - 3 . ( - 2x )

= 55x - 10x² - 3 + 6x

= - 10x² + 61x - 3

c) ( x + 1 ) ( x - 1 ) - x ( x + 2 )

= x² - 1² - x . x - x . 2

= x² - 1 - x² - 2x

= -2x - 1

d) ( 2 - 2x )² - x( 1 + 4x )

= 2² - 2 . 2 . 2x + ( 2x )² - x . 1 - x . 4x

= 4 - 8x + 4x² - x - 4x²

=4 - 7x

e) ( x - 3 )( x - 2 ) - x( x + 1 )

= x . x + x . 2 - 3 . x - 3 . ( - 2 ) - x . x - x . 1

= x² + 2x - 3x + 6 - x² - x

= - x² - 2x + 6

f) 4x² - 1 - ( 2x + 1 )²

= 4x² - 1 - [ ( 2x )² + 2 . 2x . 1 + 1²]

= 4x² - 1 - ( 4x² + 4x + 1 )

= 4x² - 1 - 4x² - 4x - 1

= - 4x - 2

Bài 2: Tìm x:

a) x( 2 - x ) + x² = - 6

⇔ x . 2 + x . ( - x ) + x² = - 6

⇔ 2x - x² + x² = - 6

⇔ 2x = -6

⇔ x = - 6 : 2

⇔ x = - 3

b) ( x - 4 )² - x( x - 7 ) = 0

⇔ x² - 2 . x . 4 + 4² - x . x - x . ( - 7 ) = 0

⇔ x² - 8x + 16 - x² + 7x = 0

⇔ - x + 16 = 0

⇔ - x = 0 - 16

⇔ - x = - 16

⇔ x = - 16 : ( - 1 )

⇔ x = 16 

c) ( x + 4 )² - x( x + 2 ) = 1

⇔ x² + 2 . x . 4 + 4² - x . x - x . 2 = 1

⇔ x² + 8x + 16 - x² - 2x = 1

⇔ 6x + 16 = 1

⇔ 6x = 1 - 16

⇔ 6x = - 15

⇔ x = $\frac{-15}{6}$ 

d) ( 15 - x ) ( 15 + x ) + ( x + 5 )² = 0

⇔ 15² - x² + x² + 2 . x . 5 + 5² = 0

⇔ 225 + 10x + 25 = 0

⇔ 10x + 250 = 0

⇔ 10x = 0 - 250

⇔ 10x = - 250

⇔ x = - 250 : 10

⇔ x = - 25

e)  x ( x - 5 ) - ( x² + x ) = x - 7

⇔ x . x + x . ( - 5 ) - x² - x = x - 7

⇔ x² - 5x - x² - x = x - 7

⇔ - 6x = x - 7

⇔ - 6x - x = - 7

⇔ - 7x = - 7

⇔ x = - 7 : ( - 7 )

⇔ x = 1

f) 5x ( x² - x + 1 ) - x² ( 5x - 5 ) - 6 = 9

⇔ 5x . x² + 5x . ( - x ) + 5x . 1 - x² . 5x - x² . ( - 5 ) - 6 = 9

⇔ 5x³ - 5x² + 5x - 5x³ + 5x² - 6 = 9

⇔ 5x - 6 = 9

⇔ 5x = 9 + 6

⇔ 5x = 15

⇔ x = 15 : 5

⇔ x = 3

Đáp án + Giải thích các bước giải:

Bài `1`: Tính

`a) 2x ( - 3x + 5 )`

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

`= - 6x^2 + 10x`

`b) ( 5x - 3 )( 1 - 2x )`

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

`= 55x - 10x^2 - 3 + 6x`

`= - 10x^2 + 61x - 3`

`c) ( x + 1 ) ( x - 1 ) - x ( x + 2 )`

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

`= x^2 - 1 - x^2 - 2x`

`= -2x - 1`

`d) ( 2 - 2x )^2 - x( 1 + 4x )`

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

`= 4 - 8x + 4x^2 - x - 4x^2`

`=4 - 7x`

`e) ( x - 3 )( x - 2 ) - x( x + 1 )`

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

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

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

`f) 4x^2 - 1 - ( 2x + 1 )^2`

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

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

`= 4x^2 - 1 - 4x^2 - 4x - 1`

`= - 4x - 2`

Bài `2`: Tìm `x:`

`a) x( 2 - x ) + x^2 = - 6`

`<=> x . 2 + x . ( - x ) + x^2 = - 6`

`<=>  2x - x^2 + x^2 = - 6`

`<=> 2x = -6`

`<=> x = - 3`

`b) ( x - 4 )^2 - x( x - 7 ) = 0`

`<=> x^2 - 2 . x . 4 + 4^2 - x . x - x . ( - 7 ) = 0`

`<=> x^2 - 8x + 16 - x^2 + 7x = 0`

`<=> - x + 16 = 0`

`<=>  x = 16` 

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

`<=>  x^2 + 2 . x . 4 + 4^2 - x . x - x . 2 = 1`

`<=>  x^2 + 8x + 16 - x^2 - 2x = 1`

`<=> 6x + 16 = 1`

`<=> 6x = - 15`

`<=> x=-15/6`

`<=> x = -5/2`

`d) ( 15 - x ) ( 15 + x ) + ( x + 5 )^2 = 0`

`<=> 15^2 - x^2 + x^2 + 2 . x . 5 + 5^2 = 0`

`<=>  225 + 10x + 25 = 0`

`<=> 10x + 250 = 0`

`<=> 10x = - 250`

`<=> x = - 25`

`e)  x ( x - 5 ) - ( x^2 + x ) = x - 7`

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

`<=>  x^2 - 5x - x^2 - x = x - 7`

`<=> - 6x = x - 7`

 `<=> - 7x = - 7`

`<=> x = 1`

`f) 5x ( x^2 - x + 1 ) - x^2 ( 5x - 5 ) - 6 = 9`

`<=>  5x^3 - 5x^2 + 5x - 5x^3 + 5x^2 - 6 = 9`

`<=> 5x - 6 = 9`

`<=> 5x = 15`

`<=>  x = 3`