Question

Factorise 27p cube -8q cube

Answer 1

Step-by-step explanation:

27p³- 8q³

➡️ (3p)³- (2q)³

➡️(3p -2q) ( 3p²+3×2 + 2q²)

➡️(3p -2q) ( 9p²+6+4q²)

Answer 2

Answer:

(3p - 2q)•(9p² + 6pq + 4q²)

Note:

★ (a + b)² = a² + 2ab + b²

★ (a - b)² = a² - 2ab + b²

★ a² - b² = (a + b)(a - b)

★ (a + b)³ = a³ + b³ + 3ab(a + b)

★ (a - b)³ = a³ - b³ - 3ab(a - b)

★ a³ + b³ = (a + b)(a² - ab + b²)

★ a³ - b³ = (a - b)(a² + ab + b²)

Solution:

27p³ - 8q³ = (3p)³ - (2q)³

= (3p - 2q)•[(3p)²+ 3p×2q + (2q)²]

= (3p - 2q)•(9p² + 6pq + 4q²)

Hence,

Required answer is :

(3p - 2q)•(9p² + 6pq + 4q²)