Final answer:
To prove that (a - b) x (a + b) = 2(a x b), we use the distributive property of multiplication and simplify both sides of the equation.
Step-by-step explanation:
To prove that (a - b) x (a + b) = 2(a x b), we can expand both sides using the distributive property of multiplication.
Expanding the left side, we get (a - b)(a + b) = a(a + b) - b(a + b).
Simplifying further, we have a^2 + ab - ab - b^2 = a^2 - b^2.
On the right side, we have 2(a x b), which represents the scalar projection of the vector a onto the vector b multiplied by the magnitude of b.
Since a^2 - b^2 is equal to the scalar projection of a onto b multiplied by the magnitude of b, we can conclude that (a - b)(a + b) = 2(a x b).