Question

Factorise x8-y8. What is the answer

Answer 1

Answer:

x⁸-y⁸ = ( x⁴)² - ( y⁴)²

= (x⁴+y⁴) (x⁴-y⁴)       [ Using identity a²-b² = (a+b) (a-b)]

= (x⁴+y⁴) [(x²)² - (y²)²]

= (x⁴+y⁴) (x²+y²) (x²-y²)

= (x⁴+y⁴) (x²+y²) (x+y) (x-y) ⇒ Answer

pls mark me the brainliest and thank me :)

Answer 2

$\boxed{x^{8}-y^{8}=(x^{4}+y^{4})(x^{2}+y^{2})(x+y)(x-y)}$

Step-by-step explanation:

Now, $x^{8}-y^{8}$

$=(x^{4})^{2}-(y^{5})^{2}$

• Hint: using $a^{mn}=(a^{m})^{n}$

$=(x^{4}+y^{4})(x^{4}-y^{4})$

• Hint: using the identity $a^{2}-b^{2}=(a+b)(a-b)$

$=(x^{4}+y^{4})[(x^{2})^{2}-(y^{2})^{2}]$

• Hint: using $a^{mn}=(a^{m})^{n}$

$=(x^{4}+y^{4})(x^{2}+y^{2})(x^{2}-y^{2})$

• Hint: using the identity $a^{2}-b^{2}=(a+b)(a-b)$

$=(x^{4}+y^{4})(x^{2}+y^{2})(x+y)(x-y)$

• Hint: using the identity $a^{2}-b^{2}=(a+b)(a-b)$

This is the required factorization.

Note:

Let us understand that the expression $(x^{8}-y^{8})$ has four factors. They are

1. $x^{4}+y^{4}$
2. $x^{2}+y^{2}$
3. $x+y$
4. $x-y$