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The expanded form of the double summation $\sum_{i=1}^{2}\sum_{j=1}^{2}x_i y_j$ is

A

$x_1 y_1 + x_2 y_2$

B

$x_1 + x_2 + y_1 + y_2$

C

$x_1 + x_2(y_1 + y_2)$

D

$x_1(y_1 + y_2) + x_2(y_1 + y_2)$

E

$x_1(y_1 + y_2) + x_2$

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