Question

Factorise: a^8-b^8
Please give your answer with solution

Answer 1

Answer:

Answer:

-a⁸ + b⁸ = (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

Step-by-step explanation:

Factorise :- a 8 + b 8

-a⁸ + b⁸

= b⁸ - a⁸

= (b⁴)² - (a⁴)²

Using x² - y² = ( x+ y)(x -y)

here x = b⁴ & y = a⁴

= (b⁴ + a⁴)(b⁴ - a⁴)

= (b⁴ + a⁴)( (b²)² - (a²)²)

= (b⁴ + a⁴)(b² + a²)(b² - a²)

= (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

-a⁸ + b⁸ =

Answer 2

Answer:

(a - b) (a + b) ( a² + b²) (a⁴ + b⁴)

Step-by-step explanation:

Solve : a⁸ - b⁸

→ (a⁴) ² - (b⁴) ²

→ By using formula = a² - b²

We get :

→ (a⁴ - b⁴) (a⁴ + b⁴)

→ (a²) ² - (b²) ² (a⁴ + b⁴)

→ By using formula = a² - b²

We get :

→ ( a² - b²) (a² + b²) (a⁴ + b⁴)

→ (a) ² - (b²) (a² + b²) (a⁴ + b⁴ )

So the answer is :

∴ (a - b) (a + b) ( a² + b²) (a⁴ + b⁴)

More To Know :

• a² - b² = (a + b) (a - b).