Question

Factorize (256x16 – 1).​

Answer 1

Step-by-step explanation:

According to BODMAS ,

Multiplication first and then subtraction :-

Therefore ; (256×16 - 1 )

4096-1

4095

Answer 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given : 256x^{16} - 1

256x 16−1

To Find : Factorize

Solution:

256x^{16}-1

256x 16−1

16x^8)^2-1^216 x 8 ) 2 −12

(16x^8+1)(16x^8-1)(16x 8+1)(16x 8−1)

(16x^8+1)[(4x^4)^2-1^2)](16x 8+1)[(4x ) 2−12)]

(16x^8+1)(4x^4+1)(4x^4-1)(16x 8+1)(4x 4+1)(4x 4 −1)

(16x^8+1)(4x^4+1)[(2x^2)^2-1^2](16x 8+1)(4x 4 +1)[(2x 2 ) 2−12 ]

(16x^8+1)(4x^4+1)(2x^2+1)(2x^2-1)(16x 8+1)(4x 4+1)(2x 2+1)(2x2−1)

Hence

256x^{16} - 1 = (16x^8+1)(4x^4+1)(2x^2+1)(2x^2-1)

256x 16 −1=(16x 8+1)(4x 4+1)(2x 2+1)(2x 2−1)