Question

the factors of x4-81​

Answer 1

Step-by-step explanation:

This is a difference of squares and, in general, factorises as follows.

a² - b² = (a - b) (a + b) -------------------------(A)

here, (x²)² = x⁴ and (9)² = 81

→ a = x² and b = 9

substituting into (A)

→ x⁴ - 81 = (x² - 9) (x² + 9) --------------------(B)

Now, the factor

x² - 9 is also a difference of squares

→ x² - 9 = (x - 3) (x + 3)

substituting into (B) complete the factorising.

→ x⁴ - 81 = (x - 3) (x + 3) (x² + 9)

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