Any maths experts/teachers can you put in to words how to explain this?

[Purplturpl]

Doing maths homework with ds and he had to simplify this (it was part of a bigger question)

3a x 2a(a + 4)

he multiplied out the brackets to get

3a x 2a^2 + 8a

i said you need to multiply the second two terms by 3a now. But he couldn’t understand why as he was following bodmas

Put brackets round the 2a(a+4) bit before expanding them.

I agree with @TickingAlongNicely in the original equation you are multiplying two terms together. In the second version, you still need to be multiplying two terms together, so you need brackets around the 2a^2 + 8a in order for it still to be considered one term.

It may be that the problem is he's forgetting that putting the 2a next to the (a+4) is multiplication just like the other. If he writes

3a x 2a x (a + 4)

does that make it clearer to him? Does he understand that those are the same?

Perhaps he thinks that he has to 'do' the brackets first because of BODMAS, but actually he isn't 'doing' the brackets, because that's addition, and he can't add the terms in the brackets together becasue they are not like terms.

So really the question is all multiplication, three terms that need to be multiplied together in whatever order he wants. He could just as easily have multiplied the 2a and the 3a together first, if he preferred. Or the 3a and the bit in brackets first. Or the last two. When you multiply something by both terms in the brackets, it still stays as a single term, so it stays in brackets.

BODMAS doesn't really come into it here, at least not in the sense that he is probably thinking about it.

The 3a and 2a should be considered to be in brackets, so effectively you have three sets of brackets to be worked out, then multiplied together.

Suggest giving "a" a number and working it through to prove it

Thank you. I knew myself that 3a needed to be multiplied by both the terms but I wasn’t sure how to explain it. Sometimes when I explain to him I worry I confuse him further