"Is there a sig. difference in amount of subunits between 2 groups according to age"

I think I've said it all in the title. I need to run right statistics to answer my question. I guess I have 2 independent variables (age in days and group code (1=experimental group; 2=control group)) and 1 dependent (amount of subunits), right?
O.K. so I found out, that I can't do a two-way ANOVA because we don't want to divide our var "age in days" into groups. The second option would probably be kind of linear regression I guess. But I received an advice that I should square some variables like age in days and multiply it with group code... I can not understand this last part. Should I really square some variables and why and which?

Anyway, if there will be anyone willing to help, I would really appreciate! And of course, I can always provide you with some more info if needed. Just let me know.