Question

factorise a cube-8bcube-64c cube-24abc​

Answer 1

Answer:

Here the given expression can be written as,

a

3

−8b

3

−64c

3

−24abc=(a)

3

+(−2b)

3

+(−4c)

3

−3(a)(−2b)(−4c)

Comparing with the given identity,

x

3

+y

3

+z

3

−3xyz≡(x+y+z)(x

2

+y

2

+z

2

−xy−yz−xz)

We get factor as

=(a−2b−4c)[(a)

2

−(−2b)

2

+(−4c)

2

−(a)(−2b)−(−2b)(−4c)−(−4c)(a)]

=(a−2b−4c)(a

2

+4b

2

+16c

2

+2ab−8bc+4ca)