Can one just use the AREA MODEL willy nilly?

Sure, computing 37 x 21 via the area model makes perfectly good sense and there is good place for this general approach in early-grade maths.

But surely you can’t use the area model in upper-grade algebra too? Afterall (3x+7)(2x+1) is fine if x=10 (it is still 37 x21), but what if x is a negative number as is allowed in algebra? You can’t have negative side lengths and negative areas in geometry!

So what’s up with using the area model in upper-school math too?

Can one use the AREA MODEL willy nilly?

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