x^4+2x^3+4x^2+4x+1因式分解？
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原式=x^4 - 2x² + 1 + 2x³ + 6x² + 4x
=(x² - 1)² + 2x(x² + 3x + 2)
=[(x+1)(x-1)]² + 2x(x+1)(x+2)
=(x+1)²(x-1)² + 2x(x+1)(x+2)
=(x+1)[(x+1)(x-1)² + 2x(x+2)]
=(x+1)[(x+1)(x²-2x+1) + 2x² + 4x]
=(x+1)(x³-2x²+x+x²-2x+1+2x²+4x)
=(x+1)(x³+x²+3x+1)
=(x² - 1)² + 2x(x² + 3x + 2)
=[(x+1)(x-1)]² + 2x(x+1)(x+2)
=(x+1)²(x-1)² + 2x(x+1)(x+2)
=(x+1)[(x+1)(x-1)² + 2x(x+2)]
=(x+1)[(x+1)(x²-2x+1) + 2x² + 4x]
=(x+1)(x³-2x²+x+x²-2x+1+2x²+4x)
=(x+1)(x³+x²+3x+1)
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