Question

$2 \sqrt{2 } \: {a}^{3} + 8 {b}^{3 } \: - 27 {c}^{3} + 18 \sqrt{2} \: abc$
Factorise​

Answer 1

Answer

We know that,

a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

Thus,

2

2

a

3

+8b

3

−27c

3

+18

2

abc

Here, a=

2

a, b=2b and c=−3c

=(

2

a+2b−3c)[(

2

a)

2

+(2b)

2

+(−3c)

2

−

2

a(2b)−(2b)(−3c)−(−3c)(

2

a)]

=(

2

a+2b−3c)(2a

2

+4b

2

+9c

2

−2

2