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(x+1)(x+2)(x+3)(x+4)+1 =(x+1)(x+4)(x+2)(x+3)+1 =(x^2+5x+4)(x^2+5x+6)+1 =(x^2+5x)^2+10(x^2++5x)+25 =(x^2+5x+5)^2
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