Question

factorise (a+b)³-(a-b)³

Answer 1

Answer:

(a+b)3-(a-b)3

Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=a+b and b=a-b.

(a+b-(a-b))((a+b)2+(a+b)(a-b)+(a-b)2)

Simplify.

Tap for more steps...

2b(3a2+b2)

Answer 2

Given :-

• (a+b)³-(a-b)³

Solution :-

Apply identity : a³ - b³ = (a - b)(a² + ab + b²)

→ (a+b)³-(a-b)³

→ [(a + b)(a - b)][(a + b)² + (a + b)(a - b) + (a - b)²]

• Identity used
• a² - b² = (a + b)(a - b)
• (a + b)² = a² + b² + 2ab
• (a - b)² = a² - b² - 2ab

→ [a² - b²][a² + b² + 2ab + a² - b² + a² + b² - 2ab]

→ [a² - b²][a² + a² + a² + b² + b² - b² + 2ab - 2ab]

→ [a² - b²][3a² + 2b²]