题目内容：

x^15+x^12+x^9+x^6+x^3+1因式分解数学题

优质解答

原式=x^12(x³+1)+x^6(x³+1)+（x³+1）
=(x³+1)(x^12+x^6+1)
=(x+1)(x²-x+1)(x^12+x^6+1)
=(x+1)(x²-x+1)(x^12+2x^6+1-x^6)
=(x+1)(x²-x+1)[(x^6+1)²-x^6]
=(x+1)(x²-x+1)(x^6+x³+1)(x^6-x³+1)
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