Question

factories using identity a³ - b³ + 1 + 3ab​

Answer 1

Using the identity

a³ + b³ + c³ - 3 a bc = (a + b + c) (a²+b²+c²-ab-ac-bc)

a³ – b³ + 1 +3ab = (a)³ +(– b) ³ + (1) ³ + 3(a)(-b) (1)

= (a-b+1) ((a) ²+(-b) ²+(1) ²- (a)(1) -(a) (-b) -(-b) (1))

=(a-b+1) (a ²+b ²+1- a + ab +b)