Question 1041509: a cubical container for shipping computer components is formed by coating a metal mold with polystyrene. If the metal mold is a cube with sides x centimeters long and the polystyrene coating is 2 centimeters thick, write an algebraic expression in terms of x that represents the volume of the polystyrene used to construct the container. Simplify the expression. (Recall: The volume V of a cube with sides of length t is given by V = t^3.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! With a cube and polystyrene 2 cm thick, each side becomes (t+4) cm thick
The volume is (t+4)^3=t^3+12t^2+48t+64.
That is through the binomial expansion.
You can foil out (t+4)^2=t^2+8t+16
multiply that by (t+4)
=t^3+4t^2+8*t^2+32t+16t+64, which is the same thing.
The volume of the metal mold is t^3
That is subtracted from the expansion, and the volume of the polystyrene is
12t^2+48t+64 units cm^3
or
4(3t^2+12t+16) units are cm^3
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can check with a cube 6 cm on a side and the polystyrene cover will be a cube 10 cm on a side
The difference between the cubes is 1000 cm^3-216 cm^3=784 cm^3
using 4(3*36+12(6)+16)=4(108+72+16)=4(196)=784 cm^3
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