1. A shipping company offers various sized shipping boxes to itscustomers. Some of these boxes are cube-shaped, with equal height,width, and depth. As part of an upcoming sales promotion, thecompany will offer two cube-shaped boxes for the price ofone.

a. Write an expression to represent the total volume of twodifferent sized boxes as a sum of cubes if one of the boxes hassides with a length of 1 foot and the other has sides with a lengthof x feet.




b. Factor the sum of cubes.




c. Calculate the total volume of the two boxes if x = 3 feet.




2. A toy manufacturer is preparing to manufacture a puzzle cube intwo different sizes. One of the puzzle cubes will have a sidelength of 4 centimeters, and the size of the other is yet to bedetermined.

a. Write an expression to represent the total volume of twodifferent sized puzzle cubes as a sum of cubes, using m centimetersas the side lengths of the second puzzle.




b. Factor the sum of cubes.




c. Calculate the total volume of the two puzzle cubes if m = 5centimeters.

3. A pet supply store is planning to offer cube-shaped fish tanks.The store manager decides to order one tank with a 12-inch sidelength but has not yet decided on the size of the other.

a. Write an expression to represent the total volume of twodifferent sized tanks as a sum of cubes, using 2t centimeters asthe length of the sides in the second tank.




b. Factor the sum of cubes.




c. Calculate the total volume of the two fish tanks if t = 7inches.





4. Think of another real-world situation involving two differentsized cube-shaped items.

a. Write a sentence to describe what the cubes represent and thenwrite an expression to represent the total volume of the two itemsas a sum of cubes, using 2a to represent the side lengths in onecube and 3b to represent the side lengths in the other cube.




b. Factor the sum of cubes.




c. Choose two different values for a and b and use these values tocalculate a specific total volume for the two items.