(x十1)4十(x十3)4一272因式分解的
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解决时间 2021-11-13 13:35
- 提问者网友：王者佥
- 2021-11-12 18:40
(x十1)4十(x十3)4一272因式分解的
最佳答案
- 五星知识达人网友：長槍戰八方
- 2021-11-12 20:10
x+2=t
(x+1)^4+(x+3)^4-272
=(t-1)^4+(t+1)^4-272
=t^4-4t^3+6t^2-4t+1+t^4+4t^3+6t^2+4t+1-272
=2t^4+12t^2-270
=2(t^4+6t^2-135)
=2(t^2+15)(t^2-9)
=2(t^2+15)(t+3)(t-3)
=2[(x+2)^2+15](x+2+3)(x+2-3)
=2(x^2+4x+4+15)(x+5)(x-1)
=2(x^2+4x+19)(x+5)(x-1)
(x+1)^4+(x+3)^4-272
=(t-1)^4+(t+1)^4-272
=t^4-4t^3+6t^2-4t+1+t^4+4t^3+6t^2+4t+1-272
=2t^4+12t^2-270
=2(t^4+6t^2-135)
=2(t^2+15)(t^2-9)
=2(t^2+15)(t+3)(t-3)
=2[(x+2)^2+15](x+2+3)(x+2-3)
=2(x^2+4x+4+15)(x+5)(x-1)
=2(x^2+4x+19)(x+5)(x-1)
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