Question

Please show me how to factor X⁴ - 1 =

Please show the steps. thank you very much, Jim

Answer 1

factoring the term
`x^4-1` we get
`\mathbf{(x^2+1)(x-1)(x+1}`

Explanation:

We need to factor the term
`x^4-1`

We know that
`a^2-b^2=(a-b)(a+b)`

We can write
`x^4 \ as \ (x^2)^2`

Simplifying:

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

Now, again using formula
`a^2-b^2=(a-b)(a+b)`

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

So, factoring the term
`x^4-1` we get
`\mathbf{(x^2+1)(x-1)(x+1}`