Step 1

To find the complete factorization of \(x^{4}−1\).

Solution:

We know that,

\(a^{2}-b^{2}=(a=b)(a-b)\)

Factorizing the given expression using above identity.

\(x^{4}-1=(x^{2})^{2}-1^{2}\)

\(=(x^{2}+1)(x^{2}-1)\)

\(=(x^{2}+1)(x^{2}-1^{2})\)

\(=(x^{2}+1)(x+1)(x-1)\)

Therefore, \(x^{4}-1=(x^{2}+1)(x+1)(x-1)\).

Step 2

Hence, complete factorization of \(x^{4}-1\ is\ (x^{2}+1)(x+1)(x-1)\).

To find the complete factorization of \(x^{4}−1\).

Solution:

We know that,

\(a^{2}-b^{2}=(a=b)(a-b)\)

Factorizing the given expression using above identity.

\(x^{4}-1=(x^{2})^{2}-1^{2}\)

\(=(x^{2}+1)(x^{2}-1)\)

\(=(x^{2}+1)(x^{2}-1^{2})\)

\(=(x^{2}+1)(x+1)(x-1)\)

Therefore, \(x^{4}-1=(x^{2}+1)(x+1)(x-1)\).

Step 2

Hence, complete factorization of \(x^{4}-1\ is\ (x^{2}+1)(x+1)(x-1)\).