Question

a³-1/a³-2a+2/a³....factorise

Answer 1

a³-1/a³-2a+2/a
=( a)³ - (1/a) ³-2a+2/a

= (a) ³- (1/a) ³-2{a-(1/a)}

now, we got a number in the form of a^3 - b^3 which equal (a-b)( a^2 + ab +b^2)

= {a -(1/a)} { a^2 + (a)(1/a) + (1/a^2)} - 2 {a -(1/a)}
= {a -(1/a)} ( a^2 + 1 + (1/a^2) -2)
= {a -(1/a)} {a^2 -1 (1/a^2)}