The expression immediately follows from a ( b+c) = ab + ac. I agree it's important that students intuitively feel that a ( b+c) = ab + ac is true. But once

The expression immediately follows from a ( b+c) = ab + ac. I agree it's important that students intuitively feel that a ( b+c) = ab + ac is true. But once we are at that, why would we even bother to teach or "proof" all variations of that expression?