Question

Find (x - 3)³+ (x + 3)³ + (- 2x)³
1. x + 5x³
2. -6x³ + 54x
3. 2x³ + 54
4. 6x³ + 7

Answer 1

Correct Answer - Option 2 : -6x³ + 54x

Given:

(x - 3)³+ (x + 3)³ + (- 2x)³

Concept

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

(a - b)(a + b) = a² - b²

Calculation

a = (x - 3), b = (x + 3) and c = -2x

⇒ 3 × (x - 3) × (x + 3) × (-2x)

⇒ 3 × (x² - 9) × (-2x)

⇒ 3 × (-2x³ + 18x)

⇒ -6x³ + 54x

∴ (x - 3)3 + (x + 3)3 + (-2x)³ is -6x³ + 54x.