Be the first to answer - "How do you factor x4-1?"

brojevnids4

Answered question

2022-12-09

How do you factor

x^{4} - 1

plautinisj4e

Beginner2022-12-10Added 4 answers

Utilize the algebraic identity to factor The expression provided is

x^{4} - 1

.
According to the algebraic identity,

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

It can be factorized as follows,

x^{4} - 1 = x^{4} - 1^{2}

\Rightarrow x^{4} - 1 = x^{2 \times 2} - 1^{2}

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

[∵ a^{m \times n} = (^{a^{m}) n}]

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

[∵ a^{2} - b^{2} = (a - b) (a + b)]

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

[∵ a^{2} - b^{2} = (a - b) (a + b)]

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