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#
