将x(x+1)(x+2)(x+3)+1配成完全平方式

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将x(x+1)(x+2)(x+3)+1配成完全平方式

x(x+1)(x+2)(x+3)+1
=[x(x+3)][(x+1)(x+2)]+1
=(x^2+3x+1-1)(x^2+3x+1+1)+1
=(x^2+3x+1)^2-1^2+1
=(x^2+3x+1)^2

x(x+1)(x+2)(x+3)+1
=[x(x+3)][(x+1)(x+2)]+1
=[x^2+3x][x^2+3x+2]+1
=(x^2+3x)^2+2(x^2+3x)+1
=(x^2+3x+1)^2

x(x+1)(x+2)(x+3)+1
=(xx+3x+2)(xx+3x)+1
=(xx+3x)^2 + 2*(xx+3x)+1
=(xx+3x+1)^2