Question

Factorise: 8(x+y)^3 + 64(2x-y)^3

Answer 1

Step-by-step explanation:

Given, 8x^3 - (2x - y) ^3  

= (2x) ^3 - (2x - y) ^3  

Using the formula:

a^3 - b^3= (a - b)(a^2 + ab + b^2) -------- eq.(1)  

Putting the value of a = 2x, b = (2x – y) in the above formula; we get  

= (2x – (2x+y)) {(2x) ^2 - 2x*(2x - y) + (2x - y) ^2}  

= y {(4x^2 - 4x^2 + 2xy + 4x^2 - 4xy + y^2)}  

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

Therefore, factorized form of the given problem is y (4x^2 - 2xy + y^2).