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

1.	Find the volume of the cuboid whose dimensions are (x + 2),(x – 1) and (x – 3).
Answer» 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 – 2x² – 5x + 6 units³

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

Answer»

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 – 2x² – 5x + 6 units³