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Question:

Factorise:(i) a⁴ - b⁴ (ii) p⁴ - 81

Solution:

(i) To factorise: a⁴ - b⁴
Now, a⁴ - b⁴ = (a²)² - (b²)² = (a² - b²)(a² + b²) = (a - b)(a + b)(a² + b²)
(ii) To factorise: p⁴ - 81
Now, p⁴ - 81 = (p²)² - (9)² = (p² - 9)(p² + 9) = (p - 3)(p + 3)(p² + 9)