Question

Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3) = 3x5 6x4 + 3x + 3x2 - 3 (Simplify your answer.)

Answer 1

Problem:

Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3)

Solution:

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

this is equivalent to:

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

this is equivalent to:

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

this is equivalent to:

`9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9`

Then, the correct answer is:

`9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9`