Question

you should solve the question solve step by step

Answer 1

We can write 256 as 4⁴

So 256x^16 = 4⁴x^16

$(256 {x}^{16} - 1) \\ = ({4}^{4} {x}^{16} - 1) \\ = > ((4 {x}^{4} ) {}^{4} - 1) \\ = > (((4x {}^{4} ) {}^{2} ) {}^{2} - (1) {}^{2} )$


using, a² - b² = (a+b)(a - b)
$((4x {}^{4}) {}^{2} - 1)((4 {x}^{4}) {}^{2} + 1) \\ \\ = > (4 {x}^{4} - 1)(4 {x}^{4} + 1)(16x {}^{8} + 1) \\ = > (2 {x}^{2} - 1)(2 {x}^{2} + 1)(4 {x}^{4} - 1)(4x {}^{4} + 1)(16 {x}^{8} + 1)$