Question

Find the following product:

(x³ + 1) (x⁶ − x^{3 +} 1)

Answer 1

Given (x³ + 1) (x⁶ − x^{3 +} 1)

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

We can rearrange the   `(x^3 + 1) (x^6 - x^3 + 1)`as

`= (x^3 + 1) [(x^3)^2 - (x^3)(1) + (1)^2]`

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

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

` = x^9 + 1^3`

` = x^9 + 1`

Hence the Product value of `(x^3 + 1) (x^6 - x^3 + 1)`is .`x^9 + 1`.