<s>[INST] Factoring $(x+1)(x+2)(x+3)(x+4)+1$ I have to factor this polynomial:
$$(x+1)(x+2)(x+3)(x+4)+1$$
WolframAlpha gives 
$$(x^2+5x+5)^2$$
How can I prove it without expanding the result?
Thanks!
 [/INST] $(x^2+5x+5)^2-1^2=(x^2+5x+4)(x^2+5x+6)=(x+1)(x+4)(x+2)(x+3)$
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