Recall that the volume of a cube is V = length x width x height. In the figure below, a cube that measures x inches by x inches by x inches is shown. Below the figure you will see a "slider". If you move the slider to the far right, you will be able to see what would happen to the cube if each edge was increased by 2 inches. Answer the questions below, referring to the figure when necessary.
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a. What is the volume of the cube before each edge is increased? (
)3 in3
b. What is the volume of cube after the edges have been increased? (
)3 in3
c. Expand and simplify the result from part b:
in3
d. Write the simplified expression that represents the amount by which the volume increased:
in3
e. Refer to the figure above. In each blank, write an expression that represents the volume of the "block" of the color indicated. Then add the volumes of all seven blocks and write your answer in the last blank.