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

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/07 04:09:48
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
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
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

先把4化掉，-2(a2+5)(a2+1)

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