Question

Factorise 27 a cube plus 8 b cube - 18 a square b - 12 a b syare

Answer 1

27a^3+8b^3-18a^b-12ab^2
3*3*3*a*a*a+2*2*2b*b*b-2*3a*3ab-2*2*3ab*b
=(3a-2b)^3 or
(3a-2b)(3a-2b)(3a-2b) answer

Answer 2

Answer : Factorized form is $(3a-2b)^3$

Step-by-step explanation:

Since we have given that

$27a^3+8b^3-18a^2b-12ab^2$

As we know the identity i.e.

$(a-b)^3=a^3+b^3-3ab(a-b)$

So, using this, we will get,

$27a^3+8b^3-18a^2b-12ab^2\\\\=(3a)^3+(2b)^3-3\times (3a)^2\times 2-3\times 3a\times (2b)^2\\\\=(3a-2b)^3$

Hence, factorized form is $(3a-2b)^3$