\(\left(\frac{5}{3}x+y\right)\left(y^2+y+3\right)=\frac{5}{3}x\left(y^2+y+3\right)+y\left(y^2+y+3\right)=\frac{5}{3}xy^2+\frac{5}{3}xy+5x+y^3+y^2+3y\)

`(5/3x +y) (y^2 +y+3)`

`= 5/3 x (y^2 +y+3)+y (y^2 +y+3)`

`= 5/3x . y^2 + 5/3x . y + 5/3 x.3 + y . y^2 + y.y +3.y`

`= 5/3 xy^2 + 5/3 xy + 5x + y^3+y^2 +3y`

(4x - 5)^2 = (4x)^2 - 2.4x.(-5) + (5)^2 = 16x^2 - 13x + 25 

(4x-5)^2

= ( 4x)^2  -  2 * 4x * 5 + 5^2

= 16x^2   - 40x   +  25

x^{n - 1} (x + y) - y (x^{n - 1} + y^{n - 1}) \(=x^n+x^{n-1}y-x^{n-1}y-y^n=x^n-y^n\)

x^n-1(x+y)-y(x^n-1+y^n-1)

= xⁿ+x^n-1y-yx^n-1-yⁿ

=xⁿ+(x^n-1y-yx^n-1)-yⁿ

=xⁿ-yⁿ

-13/2xy.(-x^2-xy-5)=-13xy.(-x^2)+(-13/2).(-xy)+(-13/2).(-5)=13x^3y+13/2x^2y^265/2xy

`( (-13)/2xy) (-x^2 - xy - 5)`

`= (-13)/2 xy . (-x)^2 +(-13)/2xy . (-xy) + (-13)/2xy . (-5)`

`= 13/2 x^3y + 13/x^2y^2 + 65/2 xy`

29³ =29 . 29 . 29 = 24389

101³ = 101.101.101 = 1030301 

HT nhé bn . sai thì thông cảm cho mình ạ 

______Vanilla______

`a, 29^3`

`= (30-1)^3`

`= 30^3 - 3 . 30^2 . 1 + 3 . 30  .1^2 +1^3`

`= 30^3 +1^3 - 3 . 30 . 1 . (30 - 1)`

`= 27 000 +1-2610`

`= 24391`

`b, 101^3`

`= (100 +1)^3`

`= 100^3 + 3 . 100^2 . 1 + 3 . 100 . 1^2+1^3`

`=100^3 +1^3 + 3 . 100 . 1 . (100+1)`

`= 1000 000 +1+30300`

`= 1030301`

a, \(a^2+2ab+b^2-5a-5b=\left(a+b\right)^2-5\left(a+b\right)\)

\(=\left(a+b\right)\left(a+b-5\right)\)

b, \(2x^3-4x^2+6x=2x\left(x^2-2x+3\right)\)

c, \(4x^2+y^2+4xy-16=\left(2x+y\right)^2-4^2=\left(2x+y-4\right)\left(2x+y+4\right)\)