Aren’t they already used in early high-school math books?
They aren’t used later on because, for more complicated expressions, manipulating the algebraic formulas is easier than the geometric method, or completely breaks down (e.g. when the powers aren’t integers or are variables)
For example, I think anybody who can visualize what (a+2b)³ or (a+b)⁴ looks like geometrically can also, and easier, do the expansion algebraically.
> Aren’t they already used in early high-school math books?
No, or at least they were not in the high-school math books I was assigned. There were no explicit referrals in any way to visual representations of the algebra involved.
They aren’t used later on because, for more complicated expressions, manipulating the algebraic formulas is easier than the geometric method, or completely breaks down (e.g. when the powers aren’t integers or are variables)
For example, I think anybody who can visualize what (a+2b)³ or (a+b)⁴ looks like geometrically can also, and easier, do the expansion algebraically.