Question

Expand $(x+1)(x^{2}+1)(x-1)$. What is the sum of the coefficients of the resulting expression?

Answer 1

1

Explanation:

(x + 1)(x² + 1)(x - 1)

= (x³ + x + x² + 1)(x - 1)

= x^4 - x³ + x² - x - x³ - x² + x - 1

= x^4 - 1

Coefficient of x^4 = 1

Answer 2

0

Explanation:

Hello, please consider the following.

For any a and b real numbers we can write.

`(a-b)(a+b)=a^2-b^2`

We apply this formula two times here, as below.

`(x+1)(x^(2)+1)(x-1)=(x+1)(x-1)(x^(2)+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1`

We have the coefficient of 1 for
`x^4` and the constant term is -1, so the sum of the coefficients is 0.

Thank you.