Question

Factorise (x-2y)³-(x+2y)³​

Answer 1

Answer:

( x - 2y)3 + (2y - 3z)3 + ( 3z - x)3

Let a = ( x - 2y), b =(2y - 3z), c= ( 3z - x)

a + b + c = ( x - 2y)+(2y - 3z)+( 3z - x) = 0

Recall that if (a + b + c) = 0 then a3 + b3 + c3 = 3abc

Thus, ( x - 2y)3 + (2y - 3z)3 + ( 3z - x)3 = 3( x - 2y)(2y - 3z)( 3z - x)