Question

factorise x to the power 8 minus 1​

Answer 1

Answer:

(x - 1)(x + 1)(x² + 1)(x⁴ + 1)

Step-by-step explanation:

Given : x⁸ - 1

We can write this as :

→ (x⁴)² - (1)²

Identity : a² - b² = (a - b)(a + b)

Here, a = x⁴, b = 1

→ (x⁴ - 1)(x⁴ + 1)

We can write this as :

→ [ (x²)² - (1)² ] (x⁴ + 1)

Identity : a² - b² = (a - b)(a + b)

Here, a = x², b = 1

→ (x² - 1)(x² + 1)(x⁴ + 1)

We can write this as :

→ [ (x)² - (1)² ] (x² + 1)(x⁴ + 1)

Identity : a² - b² = (a - b)(a + b)

Here, a = x, b = 1

→ (x - 1)(x + 1)(x² + 1)(x⁴ + 1)

Answer 2

Step-by-step explanation:

X^8-1

we can write this as (x^4)2-(1)^2

using formula (a^2-b^2)= (a+b)(a-b)

(x^4+1) (x^4-1)

we can write this as {(x^2)2-(1)2} ( x^4+1)

using formula (a^2-b^2)= (a+b) (a-b)

(x^4+1) (x^2+1) (x^2-1)

now, we can write this as

(x^4+1) (x^2+1) {(x)^2-(1)^2}

using formula (a^2-b^2)= (a+b) (a-b)

(x^4+1) (x^2+1) (x-1) (x+1)