Question

Hi please help me I suck at this.

Answer 1

The answer is option B

`V = -2(w+1)`

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

`V = (6w^2-6)/(8w^2+6w)*(4w^2 +4w)/(3-3w)*(3+4w)/(2w+2)\\\\\\`

Now simplify the expression by taking common factor

`V = (6w^2-6)/(8w^2+6w)*(4w^2 +4w)/(3-3w)*(3+4w)/(2w+2)\\\\V = (6(w^2-1))/(2w(4w+3))*(4w(w +1))/(3(1-w))*(3+4w)/(2(w+1))\\\\V = (3(w-1)(w+1))/(w(4w+3))*(4w(w +1))/(3(1-w))*(3+4w)/(2(w+1))\\\\V = (3(w-1)(w+1))/(1)*(4)/(3(1-w))*(1)/(2)\\\\V = (-3(1-w)(w+1))/(1)*(2)/(3(1-w))\\\\V = (-(w+1))/(1)*2\\\\V = -2(w+1)`

Option B