Question

factorize a^2+ c + a + a^3 - 2a^2b - 2b​

Answer 1

Answer:

Correct option is

A

(2a−b)(b−2c)(c−a)

B

3(2a−b)(b−2c)(c−a)

C

6(2a−b)(b−2c)(c−a)

a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

So, if a+b+c=0, a

3

+b

3

+c

3

=3abc

The given expression can be written as

(2a−b)

3

+(b−2c)

3

+(2c−2a)

3

We can see here that 2a−b+b−2c+2c−2a=0.

Hence, following the above concept

(2a−b)

3

+(b−2c)

3

+(2c−2a)

3

=6(2a−b)(b−2c)(c−a)

Hence, options A, B, C are correct.