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
