This was shown to me as part of a demonstration:
[n^2 (n+1)^2 + 4(n+1)^3] /4 = [(n+1)^2 [n^2 + 4(n+1)]] /4.
Presumably it should be intuitive to a lay audience, otherwise the demonstrator would have elaborated more. But I don't understand it. Could someone please describe how I can, analytically, get from the left side of this equation, to its right side?
[n^2 (n+1)^2 + 4(n+1)^3] /4 = [(n+1)^2 [n^2 + 4(n+1)]] /4.
Presumably it should be intuitive to a lay audience, otherwise the demonstrator would have elaborated more. But I don't understand it. Could someone please describe how I can, analytically, get from the left side of this equation, to its right side?
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the only that happened was (n + 1)^2 was factored out of the numerator
if you distribute the (n+1)^2 in the numerator, it will be the same again as the original
if you distribute the (n+1)^2 in the numerator, it will be the same again as the original
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too easy.
common factor ( n + 1 )^2 from left side.
(n + 1 )^2 [ n^2 + 4(n + 1 ) ] / 4
common factor ( n + 1 )^2 from left side.
(n + 1 )^2 [ n^2 + 4(n + 1 ) ] / 4