Question

Simplify:

(3x – 4y)³ + (4y – 5z)³ + (5z – 3x)³

Answer 1

Given: (3x – 4y)³ + (4y – 5z)³ + (5z – 3x)³

Step-wise calculation:

1. Let a = 3x – 4y, b = 4y – 5z, c = 5z – 3x.

Note that a + b + c = (3x – 4y) + (4y – 5z) + (5z – 3x) = 0.

2. There’s a well-known algebraic identity: If a + b + c = 0, then a³ + b³ + c³ = 3abc.

3. Therefore, (3x – 4y)³ + (4y – 5z)³ + (5z – 3x)³ = 3(3x – 4y)(4y – 5z)(5z – 3x).