Question

Find the following product:

(2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

Answer 1

In the given problem, we have to find Product of equations

Given  `(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc +8ca)`

We shall use the identity 

`x^3 + y^3 + z^3 - 3xyz = (x+y+ z) (x^2 + y^2 + z^2 - xy - yz - zx)`

` = (2a)^3 + (3b)^3 + (2c)^3 - 3 (2a )(3b)(2c)`

` = (2a) xx(2a) xx(2a) +(-3b) xx (-3b) xx(-3b)+ ( -2c) xx ( -2c) xx ( -2c) -3 (2a)(-3b)(-2c)`

` = 8a^3 - 27b^3 - 8c^3 - 36abc`

Hence the product of   `(2a - 3b - 2c)(4a^2 + 9b^2 + 4c^2 + 6ab - 6bc +8ca)` is `8a^3 - 27b^3 - 8c^3 - 36abc`.