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

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

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

( x + 1 )² - y²

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

Con ốc sên nhé bạn 

(5-y²)(5+y²)

= 5² - (y²)²

= 25 - y⁴

Áp dụng HĐT: (A-B)(A+B) = A² - B²

Sai đề rồi bạn.

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

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

(x+4)(x-4)

= x² - 4²

= x² - 16

Áp dụng HĐT: (A-B)(A+B)= A² - B²

(x+4).(x-4)

= x^2  -  4^2

=  x^2  -  16

`(x+4)(x-4)`

`=x^2 - 4^2`

`= x^2-16`

Vận dụng HĐT : `A^2 -B^2=(A-B)(A+B)`

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

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

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

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

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

(3xy+2y^2).(3xy-2y^2)

=  (3xy)^2   -  ( 2y^2)^2

=  9x^2y^2  -  4y^4

hằng đẳng thức số 3

\(a^2-b^2=\left(a+b\right).\left(a-b\right)\) công thức nha

làm:\(=\left(3xy\right)^2.\left(2y^2\right)^2=9x^2y^2.4y^4=36x^2y^6\)

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

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

`= 9x^2y^2 - 4y^4`

Vận dụng : `A^2-B^2=(A-B)(A+B)`

`(x+y+z)(x+y+z)`

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

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

Lời giải:
$(x+y+z)(x+y+z)=(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+xz)$

a: Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3\)

\(=6x^2y+2y^3\)

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

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

\(=8y^3+6y\left(x^2-y^2\right)\)

\(=8y^3+6x^2y-6y^3\)

\(=2y^3+6x^2y\)

(2/3x+3y).(3y-2/3x)

= ( 3y)^2  - ( 2/3 x )^2

=  9y^2  - 4/9 x^2

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

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

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

`= 9y^2 - 4/9 x^2`

Vận dụng : `A^2-B^2=(A-B)(A+B)`