Question

Factorise:

$(256 {x}^{16} - 1)$
Plzz give correct answer​

Answer 1

$\bold{\underline{\:ANSWER:-}}$

$\bold{\:Find\:here:-}$

• Factors of $\:(256x^{16}\:-\:1)$

$\bold{\:Explanation :- }$

$\implies\:(256x^{16}\:-\:1)$

$\implies\:(16x^8)^2-1^2$

We know ,

• $\:(x^2-y^2)\:=\:(x-y)(x+y)$

So,

$\implies\:(16x^8-1)(16x^8+1)$

$\implies\:(16x^8+1){(4x^4)^2-1^2}$

$\implies\:(16x^8+1){(4x^4+1)(4x^4-1)}$

$\implies\:(16x^8+1)(4x^4+1){(2x^2)^2-1^1 }$

$\implies\:(16x^8+1)(4x^4+1){(2x^2+1)(2x^2-1)}$

$\implies\:(16x^8+1)(4x^4+1)(2x^2+1){(\sqrt{2}x)^2-1^2}$

$\implies\:(16x^8+1)(4x^4+1)(2x^2+1)(\sqrt{2}x+1)(\sqrt{2}x-1)$

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Answer 2

Here is the answer.