230问答网 > 因式分解:1.(a2+1)2+(a2+5)2-4(a2+3)2 2.2x^4-x^3-6x^2-x+2 3.x4+y4+(x+y)4

因式分解:1.(a2+1)2+(a2+5)2-4(a2+3)2 2.2x^4-x^3-6x^2-x+2 3.x4+y4+(x+y)4

尽快,谢谢!有3道题哦!!!!!!!!!!!

2024-12-03 21:25:42

推荐回答（2个）

回答1：

①(a²+1)²+(a²+5)²-4(a²+3)²
=a4+2a²+1+a4+10a²+25-4a4-24a²-36
=-2a4-12a²-10
=-2(a4+6a²+5)
=-2(a²+1)(a²+5)
②2x4-x³-6x²-x+2
=2x4-x³-6x²+3x-4x+2
=x³(2x-1)-3x(2x-1)-2(2x-1)
=(2x-1)(x³-3x-2）
=(2x-1)[x³+x²-x²-3x-2]
=(2x-1)[x²(x+1)-(x+1)(x+2)]
=(2x-1)(x+1)(x²-x-2)
=(2x-1)(x+1)²(x-2)
③原式=2(x4+y4+3x²y²+2x³y+2xy³)
1/2原式=(x4+2x²y²+y4)+2xy(x²+y²)+x²y²
1/2原式=(x²+y²)²+2xy(x²+y²)+x²y²
1/2原式=(x²+y²+xy)²
原式=2(x²+y²+xy)²

回答2：

先把4化掉，-2(a2+5)(a2+1)