Question

.x8-1 factorize qnd give correct answer​

Answer 1

Answer:

$\red {x^{8} - 1 }\green {= (x^{4}+1)(x^{2}+1)(x-1)(x+1)}$

Step-by-step explanation:

$x^{8} - 1 \\= (x^{4})^{2} - 1^{2} \\= (x^{4} + 1)(x^{4} - 1 )$

$\boxed { \pink { a^{2} - b^{2} = (a + b)(a - b)}}$

$= (x^{4} + 1)[(x^{2})^{2} - 1^{2} ]$

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

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

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

Therefore.,

$\red {x^{8} - 1 }\green {= (x^{4}+1)(x^{2}+1)(x-1)(x+1)}$

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