Factorise $$(64x^6 - y^6)$$​​

Correct option is B

Given:

​$$(64x^6 - y^6)$$​​

Formula Used:

​$$(a^2 - b^2) = (a+b)(a-b)$$​​

​$$(a^3-b^3) = (a-b)(a^2+b^2 +ab)$$​​

​$$(a^3+b^3) = (a+b)(a^2+b^2 -ab)$$​​

Solution:

​$$(64x^6 - y^6)$$​​

​$$((2^3)^3(x^3)^2 - (y^3)^2)$$​​

​$$= ((2x)^3 - y^3)((2x)^3 + y^3)$$​​

​$$= ((2x-y)((2x)^2 +(y)^2 + (2x)(y))((2x+y)((2x)^2 +(y)^2 - (2x)(y))$$​​

​$$= ((2x-y)(4x^2 +y^2 + 2xy)((2x+y)(4x^2 +y^2 - 2xy)$$​​

​$$= (2x-y)(2x+y)(4x^2 +y^2 + 2xy)(4x^2 +y^2 - 2xy)$$​​

Hence option(b) is correct