$\begin{array}{l}a)\,\,\sin^4\alpha + \cos^4\alpha\\ = (\sin^2\alpha)^2 + 2\sin^2\alpha\cos^2\alpha +(\cos^2\alpha)^2 - 2\sin^2\alpha\cos^2\alpha\\ = (\sin^2\alpha + \cos^2\alpha)^2 - 2\sin^2\alpha\cos^2\alpha\\ = 1 - 2\sin^2\alpha\cos^2\alpha\\ b)\,\,\sin^6\alpha + \cos^6\alpha\\ = (\sin^2\alpha + \cos^2\alpha)^3 - 3\sin^2\alpha\cos^2\alpha(\sin^2\alpha + \cos^2\alpha)\\ = 1 - 3\sin^2\alpha\cos^2\alpha\end{array}$
