How does 2 ? ( ? + 1 ) + 2 ? ( ? − 1 ) simplify to 2^{1+n}n

EddyBenzen122

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I had a question in my math textbook that tells me to simplify 2 ? ( ? + 1 ) + 2 ? ( ? − 1 ).
So what I did was simplify 2 ? ( ? + 1 ) to get 2nn+2n2^nn+2^n and 2n(n1)2^n(n-1) to get 2nn2n2^nn - 2^nthen I get 2nn+2n+2nn2n2^nn+2^n+2^nn-2^n where I got stuck not knowing how i can simplify further to 2^{1+n}n
 
I had a question in my math textbook that tells me to simplify 2 ? ( ? + 1 ) + 2 ? ( ? − 1 ).
So what I did was simplify 2 ? ( ? + 1 ) to get 2nn+2n2^nn+2^n and 2n(n1)2^n(n-1) to get 2nn2n2^nn - 2^nthen I get 2nn+2n+2nn2n2^nn+2^n+2^nn-2^n where I got stuck not knowing how i can simplify further to 2^{1+n}n
I think the problem must have said to simplify 2n(n+1)+2n(n1)2^n(n+1)+2^n(n-1). Be careful when pasting, and preview the results.

Do you see that two of the terms in your expansion cancel? Then you can factor out n from the remaining two terms, and use a property of exponents to simplify further.
 
I think the problem must have said to simplify 2n(n+1)+2n(n1)2^n(n+1)+2^n(n-1). Be careful when pasting, and preview the results.

Do you see that two of the terms in your expansion cancel? Then you can factor out n from the remaining two terms, and use a property of exponents to simplify further.
I get n(2n+2n)n(2^n + 2^n) after factoring out n and I'm still stuck figuring what I should do with the exponents
 
I had a question in my math textbook that tells me to simplify 2 ? ( ? + 1 ) + 2 ? ( ? − 1 ).
So what I did was simplify 2 ? ( ? + 1 ) to get 2nn+2n2^nn+2^n and 2n(n1)2^n(n-1) to get 2nn2n2^nn - 2^nthen I get 2nn+2n+2nn2n2^nn+2^n+2^nn-2^n where I got stuck not knowing how i can simplify further to 2^{1+n}n
2n(n+1)+2n(n1)=2n{(n+1)+(n1)}=2n{2n}=n2n+1\begin{gathered} {2^n}(n + 1) + {2^n}(n - 1) = {2^n}\left\{ {(n + 1) + (n - 1)} \right\} \\ = {2^n}\left\{ {2n} \right\} \\ = n \cdot {2^{n + 1}} \\ \end{gathered}
 
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