Find the following product:
(2
(2x − y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= [2x + (−y) + 3z][(2x)2 + (−y)2 + (3z)2−(2x)(−y)−(−y)(3z) −(3z)(2x)]
= (2x)3 + (−y)3 + (3z)3 − 3(2x)(−y)(3z)
[∵ (a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc ]
= 8x3 − y + 27z3 + 18xyz