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  ${\displaystyle (2a-3b-2c)(4a^2+9b^2+4c^2+6ab-6bc+8ca)}$

We shall use the identity 

${\displaystyle x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)}$

${\displaystyle ={\left(2a\right)}^3+{\left(3b\right)}^3+{\left(2c\right)}^3-3\left(2a\right)\left(3b\right)\left(2c\right)}$

${\displaystyle =\left(2a\right)\times \left(2a\right)\times \left(2a\right)+(-3b)\times (-3b)\times (-3b)+(-2c)\times (-2c)\times (-2c)-3\left(2a\right)(-3b)(-2c)}$

${\displaystyle =8a^3-27b^3-8c^3-36abc}$

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