Factorization

Factorize: a³ + 2a²+ 2a + 1

Answer:

a³ + 2a²+ 2a + 1

= a³ + 3a²+ 3a + 1 - a² – a

= (a +1)³ – a(a + 1)

= (a + 1)[(a + 1)² – a]

= (a + 1)(a² + a + 1)

Factorize:  12a²- ab – b²

Answer:

12a²- ab – b²

= 12a²-4ab  + 3ab – b²

= 4a(3a – b) + b(3a – b)

= (4a + b)(3a – b)