Question

Without actually calculating the cube, find the value of the following:

(35)³ + (–15)³ + (–20)³

Answer 1

Given the expression: (35)³ + (–15)³ + (–20)³

Step-wise calculation:

1. Check if the sum of the numbers is zero:

35 + (–15) + (–20) = 35 – 15 – 20

35 + (–15) + (–20) = 0

2. Use the identity for cubes when the sum is zero:

If a + b + c = 0, then a³ + b³ + c³ = 3abc

3. Apply the identity with a = 35, b = –15 and c = –20:

(35)³ + (–15)³ + (–20)³ = 3 × 35 × (–15) × (–20)

4. Calculate the product inside:

3 × 35 × (–15) × (–20) = 3 × 35 × 300 

3 × 35 × (–15) × (–20) = 3 × 10,500

3 × 35 × (–15) × (–20) = 31,500