Find the following products:
i. (x- 1)(x+ 1)
ii. (x- 1)(x2 + x + 1)
iii. (x- 1)(x³ + x² + x + 1)

i. x^2 – 1

ii. x^3 – 1

iii. x^4 - 1

Step-by-step explanation:

Products are obtained by multipliyng each left term by each rigth term as follows:

i.(x- 1)(x+ 1) = (x^2  – x + x - 1) = x^2 – 1 (equal terms with opposite sign substracts and the result is 0)

ii.(x- 1)(x^2 + x + 1) = (x^3 – x^2 + x^2 – x + x – 1) = x^3 – 1

iii.(x- 1)(x³ + x² + x + 1) = (x^4 – x^3 + x^3 – x^2 + x^2 – x + x – 1) = x^4 - 1