Question

Aratati ca (x-2)(x+2)(x la a doua +4)(x la a patra+16)(x la a opta+256) = x la a 16.a - 2 la a 16.a

Answer 1

$(x - 2) \times (x + 2) \times ( {x}^{2} + 4) \times ( {x}^{4} + 16) \times ( {x}^{8} + 256) = {x}^{16} - {2}^{16} \\ ( {x}^{2} - 4) \times ( {x}^{2} + 4) \times ( {x}^{4} + 16) \times ( {x}^{8} + 256) = {x}^{16} - {2}^{16} \\ ( {x}^{4} - 16) \times ( {x}^{4} + 16) \times ( {x}^{8} + 256) = {x}^{16} - {2}^{16} \\ ( {x}^{8} - 256) \times ( {x}^{8} + 256) = {x}^{16} - {2}^{16} \\ {x}^{16} - 65536 = {x}^{16} - {2}^{16} \\ - 65536 = - {2}^{16} \\ - 65536 = - 65536$