= (x+1-y)(x+1+y)

hằng đẳng thức số 3: a^2 - b^2 = (a-b)(a+b)

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

\(\hept{\begin{cases}\frac{x+3}{x^2+4x+4}\\\frac{x+1}{3x+6}\end{cases}}MTC:3\left(x+2\right)^2\)

\(\Rightarrow\hept{\begin{cases}\frac{x+3}{x^2+4x+4}=\frac{3\left(x+3\right)}{3\left(x+2\right)^2}=\frac{3x+9}{3\left(x+2\right)^2}\\\frac{x+1}{3x+6}=\frac{\left(x+1\right)\left(x+2\right)}{3\left(x+2\right)^2}=\frac{x^2+3x+2}{3\left(x+2\right)^2}\end{cases}}\)

a) (x+y)³ - x³ - y³

= x³ + 3x²y + 3xy² + y³ - x³ -y³

= 3x²y+ 3xy²

= 3xy(x+y)

b) 4x² - y² + 4x + 1

= (2x)² + 2. 2x.1 + 1² - y²

= (2x+1)² - y²

= (2x+1-y)(2x+1+y) 

( x + y )³ - x³ - y³

= ( x + y )³ - ( x³ + y³ )

= ( x + y )³ - ( x + y )( x² - xy + y² )

= ( x + y )[ ( x + y )² - ( x² - xy + y² ) ]

= ( x + y )( x² + 2xy + y² - x² + xy - y² )

= 3xy( x + y )

a) (1-5a)^2 = 1- 10a + 25a^2

b) x^2 - 4  = (x-2)(x+2)

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

d) 4a^2 - 9= (2a - 3)(2a + 3)

Các bạn làm cả công thức hộ mình nha

\(\frac{3x}{2x+4}=\frac{3x\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}=\frac{3x^2-6x}{2\left(x+2\right)\left(x-2\right)}=\)

\(\frac{x+3}{x^2-4}=\frac{2\left(x+3\right)}{2\left(x+2\right)\left(x-2\right)}=\frac{2x+6}{2\left(x+2\right)\left(x-2\right)}\)

`(3x)/(2x+4)`

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

`= (3x^2 - 6x)/(2 (x+2) (x-2) )`

`(x+3)/(x^2 - 4)`

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

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

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

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

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

\(=x^2-x+\frac{1}{4}\)

`(x-1/2)^2`

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

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

`1,`

`(3xy -x^2 +y) 2/3 x^2y`

`= 3xy . 2/3x^2y -x^2 . 2/3 x^2y + y . 2/3x^2y`

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

`2,`

`(4x^3 - 5xy + 2x)( (-1)/2xy)`

`= 4x^3 . (-1)/2 xy - 5xy . (-1)/2xy + 2x. (-1)/2 xy`

`= -2x^4y + 5/2 x^2y^2 - x^2y`