Question

x8-81 factories please answer me​

Answer 1

Answer:

$x^{8}-81\\=(x^{4}+9)(x^{2}+3)(x+\sqrt{3})(x-\sqrt{3})$

Step-by-step explanation:

$x^{8}-81\\=(x^{4})^{2}-9^{2}\\=(x^{4}+9)(x^{4}-9)$

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

$= (x^{4}+9)[(x^{2})^{2}-3^{2})$

$= (x^{4}+9)(x^{2}+3)(x^{2}-3)$

$= (x^{4}+9)(x^{2}+3)[x^{2}-(\sqrt{3})^{2}]$

$= (x^{4}+9)(x^{2}+3)(x+\sqrt{3})(x-\sqrt{3})$

Therefore,

$x^{8}-81\\=(x^{4}+9)(x^{2}+3)(x+\sqrt{3})(x-\sqrt{3})$

•••♪

Answer 2

(x⁴ + 9) (x² + 3) (x + $\sqrt{3}$) (x - $\sqrt{3}$)

Step-by-step explanation:

Given,

x⁸ - 81

(x⁴)² - (9)²

Substituting the formula: a² - b² = (a + b) (a - b)

(x⁴ + 9) (x⁴ - 9)

(x⁴ + 9) ((x²)² - (3)²)

Substituting the formula: a² - b² = (a + b) (a - b)

(x⁴ + 9) (x² + 3) (x² - 3)

Substituting the formula: a² - b² = (a + b) (a - b)

(x⁴ + 9) (x² + 3) (x + $\sqrt{3}$) (x - $\sqrt{3}$)

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