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因式分解:(x^3-12x)^2-256
人气:463 ℃ 时间:2020-06-18 07:13:21
解答
:(x^3-12x)^2-256
=(x³-12x+16)(x³-12x-16)
=(x³+4x²-4x²-12x+16)(x³-4x²+4x²-12x-16)
=[x²(x+4)-4(x²+3x-4)][x²(x-4)+4(x²-3x-4)]
=[(x+4)x²-4(x+4)(x-1)][(x-4)x²+4(x+1)(x-4)]
=(x+4)(x²-4x+4)(x-4)(x²+4x+4)
=(x+4)(x-2)²(x-4)(x+2)²
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