To: QandQ@MathCentral.uregina.ca

Subject: factoring

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

Harley

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