How do I simplify(a-b)×(a+b), where a and b are vectors?

Answer 1

The cross product is not commutative AxB = -BxA recall in unit vectors ixj = k and jxi = -k

Then expanding out the cross product we have vectors crossed into themselves which are the zero vector and we have axb and bxa terms

The result is that the product simplifies to 2 a xb or - 2 bxa