Question

Find the volume of the cuboid whose dimensions are (x + 2), (x – 1) and (x – 3)

Answer 1

Given the dimensions of the cuboid as (x + 2), (x – 1) and (x – 3)

∴ Volume of the cuboid = (l × b × h) units³

= (x + 2)(x – 1)(x – 3) units³

We have (x + a)(x + b) (x + c) = x³ + (a + b + c)x² + (ab + bc + ca)x + abc

∴ (x + 2)(x – 1)(x – 3) = x³ + (2 – 1 – 3)x² + (2(–1) + (–1)(–3) + (–3)(2))x + (2)(–1)(–3)

= x³ – 2x² + (–2 + 3 – 6)x + 6

Volume = x³ – 2x³ – 5x + 6 units³