The full expansion method is definitely correct and is the ultimate method of solving such questions, since it lists out all the possible combinations of terms arising from the expansions.

Agreed, I think this method (though Long) will be easier to understand right ? Tho is leaves lots of room for careless mistakes since lots of exapnsion

I presume this is the easiest method to understand for most people since we have listed out the combinations and can compare a like-to-like head on comparison of terms on both sides of the equation.

A good student solving such questions should not make elementary careless mistakes for such expansions.