(3 + 1) (3² + 1) (3⁴ + 1) (3⁸ + 1) का सरलीकृत मूल्य क्या है? (3¹⁶ + 1) ?

Expression = (3 + 1) (3² + 1) (3⁴ + 1) (3⁸ + 1) (3¹⁶ + 1)

$egin{aligned} &(3-1)(3+1)left(3^{2}+1 ight) \=& frac{left(3^{4}+1 ight)left(3^{8}+1 ight)left(3^{16}+1 ight)}{(3-1)} end{aligned}$

$=frac{left(3^{2}-1 ight)left(3^{2}+1 ight)left(3^{4}+1 ight)left(3^{8}+1 ight)left(3^{16}+1 ight)}{2}$

$left[ecause(a+b)(a-b)=a^{2}-b^{2} ight]$

$=frac{left(3^{4}-1 ight)left(3^{4}+1 ight)left(3^{8}+1 ight)left(3^{16}+1 ight)}{2}$

$=frac{left(3^{8}-1 ight)left(3^{8}+1 ight)left(3^{16}+1 ight)}{2}$

$=frac{left(3^{16}-1 ight)left(3^{16}+1 ight)}{2}=frac{3^{32}-1}{2}$