adding and multiplying polynomials

Question

I need to add the following polynomials: (x^2-x+1) + (x^2-x+1)

and multiply the following: (x+1)(x^2-x+1)

Can someone explain how to do this? Thanks.

Answer 1

1) Add the polynomials

= (x^2-x+1) + (x^2-x+1)

= x^2-x+1+x^2-x+1

= 2x^2 - 2x + 2

2) Multiply the polynomial

= (x+1)(x^2-x+1)

= x*x^2+1*x^2-x*x-x*1+1*x+1*1

= x^3+x^2-x^2-x+x+1

= x^3 + 1