`E = sin^6 alpha + 3 sin^2 alpha . cos^2 alpha + cos^6 alpha`

`= (sin^6 alpha + cos^6 alpha) + 3 sin^2 alpha . cos^2 alpha`

`= ((sin^2)^3 alpha + (cos^2)^3 alpha) + 3 sin^2 alpha . cos^2 alpha`

`= (sin^2 alpha + cos^2 alpha)((sin^2)^2 alpha  - sin^2 alpha . cos^2 alpha + (cos^2)^2 alpha) + 3 sin^2 alpha . cos^2 alpha`

`= 1.(sin^4 alpha  - sin^2 alpha . cos^2 alpha + cos^4 alpha) + 3 sin^2 alpha . cos^2 alpha`

`= sin^4 alpha  - sin^2 alpha . cos^2 alpha + cos^4 alpha + 3 sin^2 alpha . cos^2 alpha`

`= sin^4 alpha  + 2 sin^2 alpha . cos^2 alpha + cos^4 alpha`

`= (sin^2 alpha + cos^2 alpha)^2`

`= 1^2`

`= 1`

Vậy `E = 1`

_________________________________

Áp dụng:

`sin^2 alpha + cos^2 alpha = 1`

Hằng đẳng thức:

`a^3 + b^3 = (a+b)(a^2 - ab + b^2)`

`(a+b)^2 = a^2 + 2ab + b^2`