Question

Find the following product:

(x² − 1) (x⁴ + x² + 1)

Answer 1

 Given `(x^2  - 1) (x^4+x^2 + 1)`

We shall use the identity  `(a-b) (a^2 + ab + b^2) = a^3 - b^3`

We can rearrange the `(x^2 - 1)(x^4 + x^2 + 1)`as

\[\left( x^2 - 1 \right)\left[ \left( x^2 \right)^2 + \left( x^2 \right)\left( 1 \right) + \left( 1 \right)^2 \right]\]

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

` = (x^2) xx(x^2) xx (x^2) - (1) xx (1) xx (1)`

` = x^6 - 1^3`

` = x^6 - 1`

Hence the Product value of `(x^2 - 1) (x^4 +x^2 + 1)`is  `x^6 - 1`.