Question

factorise the following :-

( 256x¹⁶- 1 )​

Answer 1

Answer:

(256x^16-1)

=[(16) ²x^16-1]

=........

Answer 2

Answer:

(16x^4+1) (4x^2+1) (2x+1) (2x-1)

Step-by-step explanation:

Let us use the identity a^2-b^2

So as we know 256=16^2 and 16=4^2

Now, 256x^16= (16x^4)^2

now 1^2=1

So, (16x^4)^2- 1^2

(16x^4)^2-1^2= (16x^4+1) (16x^4-1)

Now 16x^4-1= (4x^2)^2- 1

(16x^4+1) (4x^2+1) (4x^2-1)

(16x^4+1) (4x^2+1) (2x^2-1)

(16x^4+1) (4x^2+1) (2x+1) (2x-1)