Doodles Do Algebra – Lesson 64

Update: This Lesson Is Part of Book 3 of Doodles Do Algebra: “The Basic Math of Algebra” available on Amazon.

Worksheet:

Available in the book, “The Basic Math of Algebra, Book 3 of Doodles Do Algebra“

Today is the last day of polynomial multiplication, and then it is off to algebraic division.

You can brute-force this problem, but it is easier to multiply the $(n-1)$ by $(n^2+n+1)$ first and then multiply the final two resulting polynomials. This is something you can show your child after she works the problem through, or you can work it together as a group problem.
$(n^3+n^2+n-n^2-n-1)(n^3+n^2+n-n^2-n-1)=(n^3-1)(n^3-1)=n^6-n^3-n^3+1=n^6-2n^3+1$