Encyclopaedia Britannica, 11th Edition, "Geodesy" to "Geometry" / Volume 11, Slice 6

by Various

But

(a + b)a = aa + ba

by (6),

= aa + ab

by (5);

and

(a + b)b = ab + bb

by (6).

Therefore

(a + b)²	= aa + ab + (ab + bb)
	= aa + (ab + ab) + bb
	= aa + 2ab + bb