Question

Simplify:

(a – 4b)³ + (4b – 3c)³ + (3c – а)³

Answer 1

Given expression: (a – 4b)³ + (4b – 3c)³ + (3c – а)³

Step-wise calculation:

1. Let x = a – 4b, y = 4b – 3c, z = 3c – a.

2. Calculate the sum (x + y + z):

(a – 4b) + (4b – 3c) + (3c – a) = a – 4b + 4b – 3c + 3c – a

(a – 4b) + (4b – 3c) + (3c – a) = 0

3. When (x + y + z = 0), the identity for cubes applies: x³ + y³ + z³ = 3xyz.

4. Therefore, (a – 4b)³ + (4b – 3c)³ + (3c – a)³ = 3(a – 4b)(4b – 3c)(3c – a).