Question

(a+b)(a2+b2)(a4+b4)(a8+b8)(a16+b16)​

Answer 1

Ответ:

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Answer 2

It appears that you have an expression with multiple factors, each involving the sum of two terms raised to a power. To simplify this expression, you can use the following identities:

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

Let's apply these identities step by step to simplify the given expression:

$$\begin{align*} &(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^{16}+b^{16})\\ &= (a+b)((a + b)^2 - 2ab)((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)((a + b)^2 - 2ab)((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)(a+b)^2 - 2ab)((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)^3 - 2ab((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)^3 - 2ab((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)^3 - 2ab((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)^3 - 2ab((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ &= (a+b)^3 - 2ab((a^2 + b^2)^2 - 2a^2b^2)((a^4 + b^4)^2 - 2a^4b^4)((a^8 + b^8)^2 - 2a^8b^8)\\ \end{align*}$$