How do you find the volume of the box given the dimensions are: 3x + 1, 2x - 1, x + 2?

1 Answer
Aug 20, 2017

Answer:

See a solution process below:

Explanation:

The formula for the volume of a box is:

#V = l xx w xx h#

Where:

#V# is the volume

#l# is the length of the box

#w# is the width of the box

#h# is the height of the box

We can substitute to give:

#V = (color(red)(3x) + color(red)(1))(color(blue)(2x) - color(blue)(1))(color(green)(x) + color(green)(2))#

Expanding gives:

#V = ((color(red)(3x) xx color(blue)(2x)) - (color(red)(3x) xx color(blue)(1)) + (color(red)(1) xx color(blue)(2x)) - (color(red)(1) xx color(blue)(1)))(color(green)(x) + color(green)(2))#

#V = (6x^2 - 3x + 2x - 1)(color(green)(x) + color(green)(2))#

#V = (6x^2 + (-3 + 2)x - 1)(color(green)(x) + color(green)(2))#

#V = (6x^2 + (-1)x - 1)(color(green)(x) + color(green)(2))#

#V = (6x^2 - 1x - 1)(color(green)(x) + color(green)(2))#

#V = (6x^2 - x - 1)(color(green)(x) + color(green)(2))#

Expanding again gives:

#V = (6x^2 xx color(green)(x)) + (6x^2 xx color(green)(2)) - (x xx color(green)(x)) - (x xx color(green)(2)) - (1 xx color(green)(x)) - (1 xx color(green)(2))#

#V = 6x^3 + 12x^2 - x^2 - 2x - x - 2#

#V = 6x^3 + 12x^2 - 1x^2 - 2x - 1x - 2#

#V = 6x^3 + (12 - 1)x^2 + (-2 - 1)x - 2#

#V = 6x^3 + 11x^2 + (-3)x - 2#

#V = 6x^3 + 11x^2 - 3x - 2#