Answer:
The answer is option B
[tex]V = -2(w+1)[/tex]
Step-by-step explanation:
Remember that the volume of a rectangle is:
V = lwh
Where l is the length, w is the width and h is the height.
In the figure these three dimensions are given as a function of the variable w.
then the volume will be the product of the three expressions
[tex]V = \frac{6w^2-6}{8w^2+6w}*\frac{4w^2 +4w}{3-3w}*\frac{3+4w}{2w+2}\\\\\\[/tex]
Now simplify the expression by taking common factor
[tex]V = \frac{6w^2-6}{8w^2+6w}*\frac{4w^2 +4w}{3-3w}*\frac{3+4w}{2w+2}\\\\V = \frac{6(w^2-1)}{2w(4w+3)}*\frac{4w(w +1)}{3(1-w)}*\frac{3+4w}{2(w+1)}\\\\V = \frac{3(w-1)(w+1)}{w(4w+3)}*\frac{4w(w +1)}{3(1-w)}*\frac{3+4w}{2(w+1)}\\\\V = \frac{3(w-1)(w+1)}{1}*\frac{4}{3(1-w)}*\frac{1}{2}\\\\V = \frac{-3(1-w)(w+1)}{1}*\frac{2}{3(1-w)}\\\\V = \frac{-(w+1)}{1}*2\\\\V = -2(w+1)[/tex]
Option B
