← Olympiad Algebra

Chapter 1

Sum and product

Anything that doesn't change when a and b swap places can be written with a + b and ab alone. You never need a or b.

1

The square of a sum

A square of side a + b = 10. Drag the cut: a² + b² is always the whole square minus the two rectangles.

a²9b²49−ab21−ab21abab
99++4949==100100−-2⋅212 \cdot 21
Next chapter: Never negative →