Question

find the product:(x+y+2z) (x²+y²+4z²-xy-2yz-2zx

Answer 1

(x+y+2z)(x2+ y2+4z2 - xy -2yz-2zx)

= (x+y+2z)[x2+ y2+(2z)2 - xy - y(2z) - (2z)x]

= [x3+ y3+(2z)3 - 3(x)(y)(2z)]


[Using the identity, a3+b3+c3−3abc=(a+b+c)(a2+b2+c2–ab–bc–ca)]

= [x3+ y3+ 8z3 - 6xyz]