a ) ( 6x + 1 )² + ( 6x - 1 )²  - 2 . ( 6x + 1 )( 6x - 1 )

= ( 6x + 1 )² - 2 . ( 6x + 1 )( 6x - 1 ) + ( 6x - 1 )²

= ( 6x + 1 - 6x + 1 )²

= 2² = 4

b ) x . ( 2x² - 3 ) - x² . ( 5x + 1 ) + x²

= 2x³ - 3x - 5x³ - x² + x²

= ( 2x³ - 5x³ ) - 3x - ( x² - x² )

= - 3x³ - 3x

= - 3x . ( x² + 1)

bài 5:

1: \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{12x^3y^2:6xy^2}{18xy^5:6xy^2}=\dfrac{2x^2}{3y^3}\)

2: \(\dfrac{10xy-5x^2}{2x^2-8y^2}=\dfrac{5x\cdot2y-5x\cdot x}{2\left(x^2-4y^2\right)}\)

\(=\dfrac{5x\left(2y-x\right)}{-2\left(x+2y\right)\left(2y-x\right)}=\dfrac{-5x}{2\left(x+2y\right)}\)

3: \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

\(=\dfrac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)

\(=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)

4: \(\dfrac{\left(x+1\right)\left(x^2-2x+1\right)}{\left(6x^2-6\right)\left(x^3-1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-1\right)^2}{6\left(x^2-1\right)\left(x-1\right)\left(x^2+x+1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)\left(x+1\right)\cdot\left(x^2+x+1\right)}\)

\(=\dfrac{1}{6\left(x^2+x+1\right)}\)

5: \(\dfrac{2x^2-7x+3}{1-4x^2}\)

\(=-\dfrac{2x^2-7x+3}{4x^2-1}\)

\(=-\dfrac{2x^2-6x-x+3}{\left(2x-1\right)\left(2x+1\right)}\)

\(=-\dfrac{2x\left(x-3\right)-\left(x-3\right)}{\left(2x-1\right)\left(2x+1\right)}\)

\(=-\dfrac{\left(x-3\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{-x+3}{2x+1}\)

Bài 3:

1: \(9x^3-xy^2\)

\(=x\cdot9x^2-x\cdot y^2\)

\(=x\left(9x^2-y^2\right)\)

\(=x\left(3x-y\right)\left(3x+y\right)\)

2: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

3: \(x^2-3xy-6x+18y\)

\(=\left(x^2-3xy\right)-\left(6x-18y\right)\)

\(=x\left(x-3y\right)-6\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-6\right)\)

4: \(6xy-x^2+36-9y^2\)

\(=36-\left(x^2-6xy+9y^2\right)\)

\(=36-\left(x-3y\right)^2\)

\(=\left(6-x+3y\right)\left(6+x-3y\right)\)

5: \(x^4-6x^2+5\)

\(=x^4-x^2-5x^2+5\)

\(=x^2\left(x^2-1\right)-5\left(x^2-1\right)\)

\(=\left(x^2-5\right)\left(x^2-1\right)\)

\(=\left(x^2-5\right)\left(x-1\right)\left(x+1\right)\)

6: \(9x^2-6x-y^2+2y\)

\(=\left(9x^2-y^2\right)-\left(6x-2y\right)\)

\(=\left(3x-y\right)\left(3x+y\right)-2\left(3x-y\right)\)

\(=\left(3x-y\right)\left(3x+y-2\right)\)

=>6x^2-3x-10x+5-6x^2+x-12x+2=0

=>-24x+7=0

=>x=7/24

`(3x-5)(2x-1)-(x+2)(6x-1)=0`

`<=>(6x^2-3x-10x+5)-(6x^2-x+12x-2)=0`

`<=>6x^2-13x+5-6x^2-11x+2=0`

`<=>-24x+7=0`

`<=>-24x=-7`

`<=>x=7/24`

Vậy `S={7/24}`

a)

=> 6x^2 - 3x + 4x - 2 - 6x^2 + 12x = 3 

=> 13x          = 3 + 2 

=> 13x           = 5 

=> x              = 5/13 

b) ( 5x + 1 )( 6x - 2 ) = 30 x (x + 1/2 )

=> 30x^2 - 10x + 6x - 2 = 30x^2 + 15x 

=>  30x^2  - 4x - 30x^2 - 15x = 2 

=> - 19x                        = 2 

=> x                               = -2/19

(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)

<=>(6x²+27x+4x+18)-(6x²+x+12x+2)=x+1-x+6

<=>6x²+31x+18-6x²-13x-2=7

<=>18x+16=7

<=>18x=-9

<=>x=-1/2

a)

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

`<=>(x-2)^2 =1`

`<=>x-2=1` hoặc `x-2=-1`

`<=>x=3` hoặc `x=1`

b)

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

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

`<=>x-3=1`hoặc `x-3=-1`

`<=>x=4` hoặc `x=2`

c)

`4x^2 +4x+1=0`

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

`<=>2x+1=0`

`<=>x=-1/2`

d)

`9x^2 +6x+1=2`

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

\(< =>\left[{}\begin{matrix}3x+1=\sqrt{2}\\3x+1=-\sqrt{2}\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{\sqrt{2}-1}{3}\\x=\dfrac{-\sqrt{2}-1}{3}\end{matrix}\right.\)

\(\left(\frac{1}{2}-\frac{1}{3}\right).6x+6x+2=67+64\)

\(\frac{\Rightarrow1}{6}.6x+6x+2=131\)

\(\Rightarrow x+6x=131-2\)

\(\Rightarrow7x=129\)

\(\Rightarrow x=\frac{129}{7}\)