Question

Factorise :-
216a³-2√2b³​

Answer 1

Answer:

=(6a)

3

−(

2

b)

3

/* By algebraic identity */

\boxed{ \pink { x^{3} - y^{3} = (x-y)(x^{2}+xy+y^{2})}}

x

3

−y

3

=(x−y)(x

2

+xy+y

2

)

= (6a-\sqrt{2}b)[ (6a)^{2} + (6a)(\sqrt{2}b) + (\sqrt{2}b)^{2} ]=(6a−

2

b)[(6a)

2

+(6a)(

2

b)+(

2

b)

2

]

= (6a-\sqrt{2}b)(36a^{2} + 6\sqrt{2}ab + 2b^{2} )=(6a−

2

b)(36a

2

+6

2

ab+2b

2

)

Therefore.,

\red{ 216a^{3} -2\sqrt{2} b^{3} }216a

3

−2

2

b

3

\green {= (6a-\sqrt{2}b)(36a^{2} + 6\sqrt{2}ab + 2b^{2} ) }=(6a−

2

b)(36a

2

+6

2

ab+2b

2

)