因式分解竞赛题
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原式=(x+1)⁴-(x-3)⁴-256-16
=(x+1)⁴-256-(x-3)⁴-16
=[(x+1)²+16][(x+1)²-16] - (x-3)⁴-16
=[(x+1)²+16](x+1+4)(x+1-4) - (x-3)⁴-16
=(x²+2x+17)(x+5)(x-3) - (x-3)⁴-16
=(x-3)[(x²+2x+17)(x+5)- (x-3)³]-16
=(x-3)[x³+2x²+17x+5(x²+2x+17) - x³+9x²-27x+27] -16
=(x-3)(16x²+112)-16
=16[(x-3)(x²+7)-1]
=(x+1)⁴-256-(x-3)⁴-16
=[(x+1)²+16][(x+1)²-16] - (x-3)⁴-16
=[(x+1)²+16](x+1+4)(x+1-4) - (x-3)⁴-16
=(x²+2x+17)(x+5)(x-3) - (x-3)⁴-16
=(x-3)[(x²+2x+17)(x+5)- (x-3)³]-16
=(x-3)[x³+2x²+17x+5(x²+2x+17) - x³+9x²-27x+27] -16
=(x-3)(16x²+112)-16
=16[(x-3)(x²+7)-1]
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=(x^2+2x+1)^2-(x^2+7x+9)^2-272
=(x^4+4x^3+6x^2+4x+1)-(x^4+12x^3+54x^2+108x+81)-272
=8x^3+48x^2+104x-192
=(x^4+4x^3+6x^2+4x+1)-(x^4+12x^3+54x^2+108x+81)-272
=8x^3+48x^2+104x-192
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因式分解啊大哥
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