The dimensions of a rectangular prism can be expressed as x + 1, x - 2, and x + 4. In terms of x, what is the volume of the prism?
Since the formula for the volume of a rectangular prism is V = l × w × h, multiply the dimensions jointly: (x + 1)(x - 2)(x + 4). Use FOIL (First terms of each binomial multiplied, Outer terms in each multiplied and Inner terms of each multiplied, and Last term of each binomial multiplied) to multiply the ?rst two binomials: (x + 1 )(x - 2); (x • x) + x(-2) + (1 • x) + 1(-2). Simplify through multiplying inside each term: x2 - 2x + 1x - 2; combine like terms: x2 - x - 2. Multiply the third factor through this result: (x + 4)(x2 - x - 2). To do this, use the distributive property to multiply the ?rst term of the binomial, x, through each term of the trinomial, and then the second term of the binomial, 4, by each term of the trinomial: x(x2 + x + 2) 4(x2 + x + 2). Distribute: (x • x2) + (x • -x) + (x • -2) + (4 • x2) + (4 • -x) + (4 • -2). Simplify through multiplying in each term: x3 - x2 - 2x + 4x2 - 4x - 8. Use the commutative property to arrange like terms further to each other: x3 - x2 + 4x2 - 2x - 4x - 8; combine such as terms: x3 + 3x2 - 6x - 8.