Question

Simplify:
(2x + 3y + 4z) (4x^2 + 9y^2 + 16z^2 – 6xy - 12yz - 8zx)​

Answer 1

(2x + 3y + 4z) (4x^2 + 9y^2 + 16z^2 – 6xy - 12yz - 8zx)

= (2x + 3y + 4z)[(2x)²+(3y)²+(4z)²-(2x)(3y)-(3y)(4z)-(4z)(2x)]

using identity

[ (a+b+c)(a²+b²+c²-ab-bc-ca)=a³+b³+c³-3abc]

= (2x)³+(3y)³+(4z)³-3(2x)(3y)(4z)

= 8x³+27y³+64z³-72xyz