Question

Factorise : 64 (x+y)3 + 125 (2x-y)3​

Answer 1

Answer:

(9y - 6x)(156x² - 8xy + 21y²)

Step-by-step explanation:

Factorise:

64(x + y)³ + 125(2x - y)³

Solution:

☆ a³- b³= (a - b)(a² + ab + b²)

64(x + y)³ + 125(2x - y)³

= [ 4(x + y) ]³ + [ 5(2x - y) ]³

= (4x + 4y)³ + (10x - 5y)³

= [ (4x + 4y) - (10x - 5y) ] [ (4x + 4y)² + (4x + 4y)(10x - 5y) + (10x - 5y)² ]

= (4x - 10x + 4y + 5y)(16x² + 32xy + 16y² + 40x² - 20xy + 40xy - 20y² + 100x² - 100xy + 25y²)

= (9y - 6x)(156x² - 8xy + 21y²)

Answer 2

Step-by-step explanation:

☆ a³- b³= (a - b)(a² + ab + b²)

64(x + y)³ + 125(2x - y)³

= [ 4(x + y) ]² + [ 5(2x - y) ]³

= (4x + 4y)³ + (10x - 5y)³

= [ (4x + 4y) - (10x - 5y) ] [ (4x+4y)² + (4x + 4y)

(10x - 5y) + (10x - 5y)²]

- (4x - 10x + 4y + 5y)(16x² + 32xy + 16y² + 40x² -

20xy + 40xy - 20y² + 100x² - 100xy + 25y²)

= (9y - 6x)(156x² - 8xy + 21y²)