Tính giá trị biểu thức sin6a + cos6a +3sin2a . cos2a (a là alpha)

`~rai~`

\(\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha\cos^2\alpha\\=(\sin^6\alpha+\cos^6\alpha)+3\sin^2\alpha\cos^2\alpha\\=(\sin^2\alpha+\cos^2\alpha)(\sin^4\alpha-\sin^2\alpha\cos^2\alpha+\cos^4\alpha)+3\sin^2\alpha\cos^2\alpha\\=\sin^4\alpha-\sin^2\alpha\cos^2\alpha+\cos^4\alpha+3\sin^2\alpha\cos^2\alpha\\=(\sin^4\alpha+2\sin^2\alpha\cos^2\alpha+\sin^4\alpha)-3\sin^2\alpha\cos^2\alpha+3\sin^2\alpha\cos^2\alpha\\=(\sin^2\alpha+\cos^2\alpha)^2\\=1^2=1.\\\text{Giải thích:Công thức áp dụng:}\\+)\sin^2\alpha+\cos^2\alpha=1.\\\text{+)Hằng đẳng thức:}A^3+B^3=(A+B)(A^2-AB+B^2).\)