Question

Find the product `(2a-3b-2c)(4a^(2)+9b^(2)+4c^(2)+6ab-6bc+4ca)`.

Answer 1

`[2a+(-3b)+(-2c)][(2a)^(2)+(-3b)^(2)+(-2c)^(2)-2axx(-3b)-(-3b)(-2c)-(2a)(-2c)]`
`(x+y+z)(x^(2)+y^(2)+z^(2)-xy-yz-zx) " " ("where" x=2a, y=-3b " and" z=-2c)`
`=x^(3)+y^(3)+z^(3)+3xyz=(2a)^(3)+(-3b)^(3)+(-2c)^(3)-3xx2axx(-3b)xx(-2c)`
`=8a^(3)-27b^(3)-8c^(3)-36abc`