Try to write what you know about both. Then, when you've done this, write about how they're different and the same. For example: "In basketball, the ball is aimed into a 'basket' and thrown in. In football however, the ball is carried into one of the areas on the field, the endzone, where the point is then counted. Both games involve scoring points on a team, just in different ways." Hope this helped!
Answer: make the best use of.
Explanation:
The meaning of the word <em>maximize</em> in this case is: to use (something) in a way that will give the best result. The student mentions that he has limited amount of time for homework, so he wants to use the time available in a best possible way.
The synonyms of this verb that could be used in this sentence are: <em>make the most of, make the best use of</em>, etc. In other contexts, synonyms for <em>'maximize'</em> are <em>increase, make bigger, enlarge</em>, etc.