Find the volume of the box. Use the formula V = lwh.?

Question

The dimensions are:
3x + 1
2x - 1
x + 2

Answer 1

The volume is lwh [length × width × height]

Length = 3x + 1, width = 2x - 1 and height = x + 2.

V = (3x + 1)(2x - 1)(x + 2).

FOIL method: the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms and the Last terms.

V = [3x(2x) + 3x(-1) + 1(2x) + 1(-1)](x + 2)

V = [6x² - 3x + 2x - 1][x + 2]

V = [6x² - x - 1][x + 2]

V = [6x²(x) - x(x) - 1(x)] + [6x²(2) - x(2) - 1(2)]

V = 6x³ - x² - x +12x² - 2x - 2

V = 6x³ + 11x² - 3x - 2

Therefore Volume V = 6x³ + 11x² - 3x - 2.