Question

(a+b)(a2+b2)(a4+b4)(a8+b8)(a16+b16)=?​

Answer 1

Ответ:

${a}^{5} {b}^{5} (1 + 1)(2 + 2)(4 + 4)(8 + 8)(16 + 16) = {a}^{5} {b}^{5} \times 32 \times 16 \times 32 = 16384 \: {a}^{5} {b}^{5}$

Объяснение:

●《☆Я смог помочь!?☆》●

Answer 2

Expanding the expression $(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^{16}+b^{16})$ would result in a very long and complex expression. However, you can notice a pattern that emerges as you expand it. Each term in the expansion will be of the form $a^{2^n} + b^{2^n}$ where $n$ is a non-negative integer.

Here are the first few terms:

$(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^{16}+b^{16})$ = $(a^{2^0} + b^{2^0})(a^{2^1} + b^{2^1})(a^{2^2} + b^{2^2})(a^{2^3} + b^{2^3})(a^{2^4} + b^{2^4})$

= $(a^1 + b^1)(a^2 + b^2)(a^4 + b^4)(a^8 + b^8)(a^{16} + b^{16})$

= $a^{2^0+2^1+2^2+2^3+2^4} + b^{2^0+2^1+2^2+2^3+2^4}$

= $a^{31} + b^{31}$

So, the expanded expression is $a^{31} + b^{31}$.