Question

Factorize each of the following expressions:
a³+3a²b³+3ab²+b³-8

Answer 1

=a³ + 3a² b + 3a b² + b^³ = 8

={a³ + 2a² b + ab²} + { a² b + 2a b² + b²} = 8

=a{a² + 2ab + b²} + b{a² + 2ab + b²} = 8

= {a + b} {a² + 2ab + b²} = 8

= { a + b } { a² + ab + ab + b² } = 8

{ a + b } { a ( a + b ) + b ( a + b ) } = 8

= { ( a + b )( a + b )² } = 8

= ( a + b )³ = 8

∴ a + b = 2

THANKS.....