Simplify algebraic expressions

Algebra

Simplify algebraic expressions

Postby Guest » Sun Nov 01, 2020 1:18 pm

Could someone please help me with this?

Simplify:
(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)(a^32+b^32)(a^64+b^64)
I know it got to be something with difference of squares, but i'm not sure what should I do here
Thank you in advance
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Re: Simplify algebraic expressions

Postby nathi123 » Mon Nov 02, 2020 5:14 am

[tex]A=(a+b).(a^{2}+b^{2}).(a^{4}+b^{4}).(a^{8}+b^{8}).(a^{16}+b^{16}).(a^{32}+b^{32}).(a^{64}+b^{64}).\frac{a-b}{a-b}[/tex]
[tex]A=\frac{(a^{2}-b^{2})}{a-b}.(a^{2}+b^{2}).(a^{4}+b^{4}).(a^{8}+b^{8}).(a^{16}+b^{16}).(a^{32}+b^{32}).(a^{64}+b^{64})[/tex]
[tex]A=\frac{(a^{4}-b^{4}).(a^{4}+b^{4})(a^{8}+b^{8}).(a^{16}+b^{16}).(a^{32}+b^{32}).(a^{64}+b^{64})}{a-b}[/tex]
[tex]A=\frac{(a^{8}+b^{8})(a^{8}+b^{8}).(a^{16}+b^{16}).(a^{32}+b^{32}).(a^{64}+b^{64})}{a-b}=\frac{(a^{16}-b^{16})(a^{16}+b^{16}).(a^{32}+b^{32}).(a^{64}+b^{64})}{a-b}[/tex]
[tex]A=\frac{(a^{32}-b^{32}).(a^{32}+b^{32}).(a^{64}+b^{64})}{a-b}=\frac{(a^{64}-b^{64}).(a^{64}+b^{64})}{a-b}=\frac{a^{128}-b^{128}}{a-b}.[/tex]

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