Question

Factorise 64x^6-y^6
please​

Answer 1

Answer:

Refer the picture

Answer 2

Answer: (2x + y) (2x − y) (4x² + y² + 2xy) (4x² + y² − 2xy)

Solution:

64x⁶ −  y⁶

= [(4x²)³ −  (y²)³

= [(4x² −  y²)] [ (4x²)² + (4x² × y²) + (y²)² ]

Identity:

• (a³ − b³) = (a −  b) (a² + ab + b²)
• a = 4x², b = y²

= [ (2x)² −  y² ] [ (4x²)² + 2 (4x²y²) + (y²)² − 4x²y² ]

= [ (2x + y) (2x − y) ] [ (4x² + y²)² − 4x²y² ]

Identities:

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

= [ (2x + y) (2x − y) ] [ (4x² + y²)² − (2xy)²]                  [ 4x²y² = (2xy)² ]

=  [ (2x + y) (2x − y) ] [ (4x² + y² + 2xy) (4x² + y² − 2xy)

Identity:

• a² − b² = (a + b) (a − b)
• a = 4x² + y² , b = 2xy

= (2x + y) (2x − y) (4x² + y² + 2xy) (4x² + y² − 2xy)

Hope you understood.

Thank You.