Factorize each of the following expressions:$8x^3y^3 + 27a^3$

Given:

$8x^3y^3 + 27a^3$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

$8x^3y^3 + 27a^3 = (2xy + 3a) [(2xy)^2 - 2xy \times 3a + (3a)^2]$

$= (2xy + 3a) (4x^2y - 6xya + 9a^2)$

Hence, $8x^3y^3 + 27a^3 = (2xy + 3a) (4x^2y - 6xya + 9a^2)$.