By using binomial theorem, expand: `(1+x+x^2)^3` (b) `(1-x+x^2)^4`

Explanation

Let `y=x+x^2`

Then, `(1+x+x^2)^3`

=`(1+y)^3=3_(C_0)​+3_(C_1)​+3_(C_2)y^2​+3_(C_3)​y^3`

=`1+3y+3y^2+y^3`

=`1+3(x+x^2)+3(x+x^2)^2+(x+x^2)^3`

=`1+3(x+x^2)+3(x^2+2x^3+x^4)+{3_(C_0)​x^3(x^2)^0+3_(C_1)​(x^2)(x^2)^1+3_(C_2)​x^1(x^2)^2+3_(C_3)​(x^2)3}`

=`1+3(x+x^2)+3(x^2+2x^3+x^4)+(x^3+3x^4+3x^5+x^6)`

=`x^6+3x^5+6x^4+7x^3+6x^2+3x+1`