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Cubes Within Cubes Revisited

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Partitioning Revisited

Age 11 to 14
Challenge Level

We can show that $14^2 = 196$ by considering the area of a $14$ by $14$ square:

We can show that $(x + 1)^2 \equiv x^2 + 2x + 1$ by considering the area of an $(x + 1)$ by $(x + 1)$ square:
Show in a similar way that $(x + 2)^2 \equiv x^2 + 4x + 4$.

Then use the same method to evaluate $(x + 3)^2$ and $(x + a)^2$.