Name: A.R.

Who is asking: Student
Level: Secondary

Question:
These questions deal with factoring.

(1+z+z^2)^2 and (p^2-pq+q^2)^2

I partially understand the second line which would be 1+z^2+z^4+2z+2z^2+2z^3 but I don't understand where the 2 comes from in the second half of that line.

p.s.(^2 means squared or cubed etc.)

Please help me out A.S.A.P.!
I have a quiz on this tomorrow!
Thank-you,
A.R.

Hi A.R.
To expand (1+z+z^2)^2 think of (1+z+z^2)(1+z+z^2).

• First multiply the 1 in the first factor times the second factor to get
  1(1+z+z^2)=1+z+z^2

• Second multiply the z in the first factor times the second factor to get
  z(1+z+z^2)=z+z^2+z^3

• Third multiply the z^2 in the first factor times the second factor to get
  z^2(1+z+z^2)=z^2+z^3+z^4

• Finally add the results of the 3 previous steps to get
  (1+z+z^2)^2
  =(1+z+z^2)+(z+z^2+z^3)+(z^2+z^3+z^4)
  =1+2z+3z^2+2z^3+z^4