If $a, b, c, d$ are continued proportional, then $(a^2+$ equals—

With $\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$, the products $ab,\,bc,\,cd$ behave like a geometric chain so that the cross terms align perfectly. The expression is therefore the perfect square $(ab+bc+cd)^2$.