Hi Gise!
We use "will" in many situations:
- to predict future events which are not already decided or obviously on the way. eg.: "I think Liverpool will win"
- to tell people about a decision as we make it, for instance if we are agreeing to something. E.g.: "Ok. We �ll buy the tickets if you �ll buy supper after the show." or "The phone is ringing. I �ll answer it." (You make the decision at the moment of speaking, not before)
"Going to" often emphasises the idea of intention, of a decision that has already been made. Eg.: "We �re going to get a new car soon." / "I �m going to keep asking her out until she says �Yes �".
About your sentences, now.
The 1st one, I would definitely say "I will help you. Let �s start." (not "going to" because it �s a decision you make at the moment of speaking, not something you have decided before)
2nd one: I think both are possible. I think it depends on the situation. If Alexander decided to take those shorts at the right moment when the shop assistant asked him, I would choose "will", but if Alexander have already seen other shorts in the shop and seen the red ones and previously decided he would buy those and not other ones, then I would have to say to use "going to". (However, I think the 1st situation is more common
! So "will" is right.)
I hope this helps.
Hugs from Portugal,
Patr�cia
P.S.: By the way, I used "Practical English Usage", by Michael Swan, to give the grammar explanations and examples. It�s a great grammar book to explain things like this.
. If you know any �trick � to identify when to use �will � and when �be going to �, please let me know!!! Thanks in advance!
