Question

Find (w² + 1)(w³ - w + 1).

Answer 1

Product is
`w^5+w^2-w+1`

Explanation:

Given:
`(w^2+1)(w^3-w+1)`

Simplify the product of polynomial.

It is product of binomial with trinomial.

`\Rightarrow (w^2+1)(w^3-w+1)`

`\Rightarrow w^2(w^3-w+1)+1(w^3-w+1)` (Distributive property)

`\Rightarrow w^2\cdot w^3-w^2\cdot w+w^2\cdot 1+w^3-w+1` (Distributive property)

`\Rightarrow w^5-w^3+w^2+w^3-w+1` (combine like term)

`\Rightarrow w^5+w^2-w+1`

Product is
`w^5+w^2-w+1`