Question

The algebraic expression (a+b)^2, in which a and b are both unequal positive numbers, can be represented by a single square composed of two squares and two rectangles as shown in the figure. If the expression (a+b+c)^2 were represented by the figure of this kind, it would be composed of 3 squares and

(A) no rectangles
(B) 2
(C) 3
(D) 4
(E) 6

Im guessing C...

Answer 1

\[
(a+b+c)^2=(a+b+c)(a+b+c)=a^2+2ab+2ac+b^2+2bc+c^2
\]

Answer 2

\(2+2+2=6\)