Question

Factorize 27 ( x + y )³ + 8 ( 2x - y )³
asap

Answer 1

Given :-

➪ To factorize 27 ( x + y )³ + 8 ( 2x - y )³

Solution :-

➪ Let (x + y) = a

➪ Let (2x - y) = b

➪ 27a³ + 8b³

➪ (3a)³ + (2b)³

Identity used :-

➪ a³ + b³ = (a + b) (a² - ab + b²)

➪ a = 3a and b = 2b

➪ (3a + 2b) (9a² - 6ab + 4b²)

➪ [3(x+y) + 2(2x-y)] [9(x+y)² - 6(x+y) (2x-y) + 4(2x-y)]²

➪ (7x + y) (13x² + 19y² - 4xy) is the final answer

Know more :-

➪ (a + b)³ = a³ + b³ + 3ab(a+b)

➪ (a - b)³ = a³ - b³ - 3ab(a-b)

➪ a³ - b³ = (a-b) (a² + ab + b²)

Answer 2

Given :-

➪ To factorize 27 ( x + y )³ + 8 ( 2x - y )³

Solution :-

➪ Let (x + y) = a

➪ Let (2x - y) = b

➪ 27a³ + 8b³

➪ (3a)³ + (2b)³

Identity used :-

➪ a³ + b³ = (a + b) (a² - ab + b²)

➪ a = 3a and b = 2b

➪ (3a + 2b) (9a² - 6ab + 4b²)

➪ [3(x+y) + 2(2x-y)] [9(x+y)² - 6(x+y) (2x-y) + 4(2x-y)]²

➪ (7x + y) (13x² + 19y² - 4xy) is the final answer

Know more :-

➪ (a + b)³ = a³ + b³ + 3ab(a+b)

➪ (a - b)³ = a³ - b³ - 3ab(a-b)

➪ a³ - b³ = (a-b) (a² + ab + b²)