Question

factor the following sum of two cubes: z^3+27. so far i have: (z+3)(x^2....

Answer 1

That is a good start :-)

Answer 2

Do you know the formula?

Answer 3

First write it as a "sum of two cubes."

Answer 4

z^3+3^3

Answer 5

is it (z+3)(x^2-3z+9)

Answer 6

see a^3 +b^3 =(a+b)(a^2 -ab +b^2)

Answer 7

yup correct

Answer 8

do u want to factorise further...

Answer 9

then if w be the complex cube root of unity then w^2+w=-1 and w^3=1
hence
a^2 -ab +b^2=a^2 +(w^2+w)ab +b^2w^3
=a^2 +w^2ab+wab +b^2w^3
=a(a+bw^2) +bw(a+bw^2)
=(a+bw^2)(a+bw)