Question

Помогите найти выражение, пожалуйста. ​

Answer 1

Ответ:

$(a - b)(a + b) = {a}^{2} - {b}^{2}$

$\displaystyle (a - 1)(a + 1)( {a}^{2} + 1)( {a}^{4} + 1)( {a}^{8} + 1)( {a}^{16} + 1) - {a}^{32}$

1.

$(a - 1)(a + 1) = {a}^{2} - {1}^{2} = {a}^{2} - 1$

$( {a}^{2} - 1)( {a}^{2} + 1)( {a}^{4} + 1)( {a}^{8} + 1)( {a}^{16} + 1) - {a}^{32}$

2.

$( {a}^{2} - 1)( {a}^{2} + 1) = { ({a}^{2} )}^{2} - {1}^{2} = {a}^{2 \times 2} - 1 = {a}^{4} - 1$

$( {a}^{4} - 1)( {a}^{4} + 1)( {a}^{8} + 1)( {a}^{16} + 1) - {a}^{32}$

3.

$( {a}^{4} - 1)( {a}^{4} + 1) = { ({a}^{4} )}^{2} - {1}^{2} = {a}^{4 \times 2} - 1 = {a}^{8} - 1$

$( {a}^{8} - 1)( {a}^{8} + 1)( {a}^{16} + 1) - {a}^{32}$

4.

$( {a}^{8} - 1)( {a}^{8} + 1) = {( {a}^{8} )}^{2} - {1}^{2} = {a}^{8 \times 2} - 1 = {a}^{16} - 1$

$( {a}^{16} - 1)( {a}^{16} + 1) - {a}^{32}$

5.

$( {a}^{16} - 1)( {a}^{16} + 1) = {( {a}^{16}) }^{2} - {1}^{2} = {a}^{32} - 1$

$( {a}^{32} - 1) - {a}^{32} = {a}^{32} - 1 - {a}^{32} = - 1$

ответ: -1