Answer
$$\sin^3\alpha+\cos^3\alpha=(\sin\alpha+\cos\alpha)(1-\sin\alpha\cos\alpha)$$
Work Step by Step
$$A=\sin^3\alpha+\cos^3\alpha$$
Now it is crucial here not to forget that $$a^3+b^3=(a+b)(a^2-ab+b^2)$$
which means
$$A=(\sin\alpha+\cos\alpha)(\sin^2\alpha-\sin\alpha\cos\alpha+\cos^2\alpha)$$
$$A=(\sin\alpha+\cos\alpha)[(\sin^2\alpha+\cos^2\alpha)-\sin\alpha\cos\alpha]$$
- From Pythagorean Identity: $$\sin^2\alpha+\cos^2\alpha=1$$
So, $A$ would be $$A=(\sin\alpha+\cos\alpha)(1-\sin\alpha\cos\alpha)$$
