Theo bạn:

`A = sin^6x + cos^6x + 3sin^2x - cos^2x`

` = ( sin^2x + cos^2x )( sin^4x - cos^2xsin^2x + cos^4x ) + 3sin^2x -cos^2x`

`= sin^4x - sin^2xcos^2x + cos^4x + 3sin^2x - cos^2x`

`= ( sin^2x + cos^2x )^2 - 3sin^2xcos^2x + 3sin^2x - cos^2x`

`= 1^2 + 3sin^2x( 1 - cos^2x ) - cos^2x`

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

`= sin^2x + 3sin^4x`

Vậy `A =  sin^2x + 3sin^4x`

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Theo mình nên sửa thành

`A=sin^6x+cos^6x+3sin^2xcos^2x`

`=(sin^2x)^3+(cos^2x)^3+3sin^2xcos^2x . 1`

`=(sin^2x)^3+(cos^2x)^3+3sin^2xcos^2x(sin^2x+cos^2x)`

`=(sin^2x+cos^2x)^3`

`=1`

Vậy `A=1`