Question

Factorise a^8 - b^8 who will do I will mark as brainlist

Answer 1

Given Equation is a^8 - b^8

It can be written as,

= > (a^4)^2 - (b^4)^2

We know that a^2 - b^2 = (a + b)(a - b)

= > (a^4 + b^4)(a^4 - b^4)

= > (a^4 + b^4)((a^2)^2 - (b^2)^2)

= > (a^4 + b^4)(a^2 + b^2)(a^2 - b^2)

= > (a^4 + b^4)(a^2 + b^2)(a + b)(a - b).

We know that a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2

= $= > (a^2 + b^2)^2 - (\sqrt{2}ab)^2$

$= > ((a^2 + b^2) - \sqrt{2}ab)((a^2 + b^2) + \sqrt{2}ab)$

$= > (a^2 + b^2 - \sqrt{2}ab)(a^2 + b^2 + \sqrt{2}ab)$

Therefore, the final answer is:

$= > (a - b)(a + b)(a^2 + b^2)(a^2 + b^2 + \sqrt{2}ab)(a^2 + b^2 - \sqrt{2}ab)$

Hope this helps!

Answer 2

Given Equation is a^8 - b^8

It can be written as,

= > (a^4)^2 - (b^4)^2

We know that a^2 - b^2 = (a + b)(a - b)

= > (a^4 + b^4)(a^4 - b^4)

= > (a^4 + b^4)((a^2)^2 - (b^2)^2)

= > (a^4 + b^4)(a^2 + b^2)(a^2 - b^2)

= > (a^4 + b^4)(a^2 + b^2)(a + b)(a - b).

Please mark it as brainliest answer

Hope it helped you