问一个初中数学题...帮个忙吧...这个题是这样的..分解因式:(a+1)(a+1)(a+1)(a+1)+(a+3)(a+3)(a+3)(a+3)-272
问题描述：
问一个初中数学题...帮个忙吧...
这个题是这样的..
分解因式:
(a+1)(a+1)(a+1)(a+1)+(a+3)(a+3)(a+3)(a+3)-272
答
=(a+1)^4+(a+3)^4-272
=a^4+1+4a^2+a^4+36a^2+81-272
=2a^4+89+40a^2-272
=2a^4-183+40a^2
答
=(a+1)^4+(a+3)^4-272
=(a^4+4a^3+6a^2+4a+1)+(a^4+12a^3+54a^2+108a+81)-272
=2a^4+16a^3+60a^2+112a-190
答
=(a+1)^4+(a+3)^4-272
设出Y=a+1+a+3/2=a+2
原式=(y-1)4+(y+1)4-272
=2(y4+6y2+1)-272
=2(y4+6y2-135)
=2(y2-9)(y2+15)
=2(y+3)(y-3)(y2+15)
=2(x+5)(x-1)(x2+4x+19)