Question

Resolve into factors a³+b³+3ab(a+b)-8​

Answer 1

a³ + b³ + 3ab(a+b) - 8

(Using Identity, (a+b)³ = a³ + b³ + 3ab(a+b) )

= (a+b)³ - 2³

(Using, x³ - y³ = (x - y)( x² + y² + xy) )

= (a+b - 2) ((a+b)² + 2² + 2(a+b) )

= (a+b-2)(a² + b² + 2ab + 4 + 2a + 2b)