Question

Factorise(a+b)³-a-b. [5star+Bralliant answer].

Answer 1

 ( a + b )³ - ( a + b )

By taking ( a + b ) as common,

 = ( a + b ) { ( a + b )² - 1 }
= ( a + b ) { ( a + b )² - 1² }
= (a+b) ( a+b-1) (a+b+1)

its because of the property :- x²-y² = (x-y)(x+y)
here x is ( a + b )
and y is (1)

Answer 2

$( {a}^{3} +3 {a}^{2} b + 3a {b }^{2} + {b}^{3} ) - a - b = \\ {a}^{3} +3 {a}^{2} b + 3a {b }^{2} + {b}^{3} - a - b$