   Chapter 13.6, Problem 55E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONSDifference in Volume of Cubes The volume of a cube of side x inches is given by V ( x ) = x 3 , so the volume of a cube of side x + 2 inches is given by V ( x + 2 ) = ( x + 2 ) 3 .Use the Binomial Theorem to show that the difference in volume between the larger and smaller cubes is 6 x 2 + 12 x + 8 cubic inches.

To determine

To show:

The difference in volumes are 6x2+12x+8in3.

Explanation

Given:

V(x)=x3in3 and V(x+2)=(x+2)3in3.

Approach:

The Binomial theorem is given by

(a+b)n=Cn0anb0+Cn1an1b1+Cn2an2b2++Cnna0bn.

Calculation:

Consider

V(x+2)=(x+2)3in3=[C30x3<

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