Question

5. Factorise the following:
(i) x8 -y8​

Answer 1

Answer:

(x⁴ + y⁴)(x² + y²)(x + y)(x - y)

Step-by-step explanation:

Given : x⁸ - y⁸

We can write this as :

→ (x⁴)² - (y⁴)²

Identity : a² - b² = (a + b)(a - b) Here, a = x⁴, b = y⁴

→ (x⁴ + y⁴)(x⁴ - y⁴)

We can write this as :

→ (x⁴ + y⁴) [ (x²)² - (y²)² ]

Identity : a² - b² = (a + b)(a - b) Here, a = x², b = y²

→ (x⁴ + y⁴)(x² + y²)(x² - y²)

We can write this as :

→ (x⁴ + y⁴)(x² + y²) [ (x)² - (y)² ]

Identity : a² - b² = (a + b)(a - b) Here, a = x, b = y

→ (x⁴ + y⁴)(x² + y²)(x + y)(x - y)