Question

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

Answer 1

Answer:

(x4+y4) (x2+y2) (x+y) (x-y)

Step-by-step explanation:

x8-y8=(x4)2-(y4)2

(x4+y4)(x4-y4)

(x4+y4)(x2)2-(y2)2

(x4+y4)(x2+y2)(x+y)(x+y)

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Answer 2

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)