数学急～～高手帮帮忙

来源：百度知道 编辑：UC知道 时间：2024/06/03 02:22:30
因式分解：
（1）(x^2+3x+2)(4x^2+8x+3)-90
(2) x^4-7x^2+1
(3) x^3+2x^2-5x-6
(4) x^4+y^4+(x+y)^4

(x^2+3x+2)(4x^2+8x+3)-90
=（x+2）（x+1）（2x+1）（2x+3）-90
=（x+2）（2x+1）（x+1）（2x+3）-90
=（2x^2+5x+2）(2x^2+5x+3)-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)

x^4-7x^2+1
=x^4-2x^2+1-5x^2
=(x^2-1)^2-(√5x)^2
=(x^2-1+√5x)(x^2-1-√5x)
=(x^2+√5x-1)(x^2-√5x-1)

原式=X^3+2X^2+X-X-5X-6
=(X^3+2X^2+X)+(-X-5X-6)
=X(X^2+2X+1)+(-6X-6)
=X(X+1)^2-6(X+1)
=(X+1)(X^2+X-6)
=(X+1)(X-2)(X+3)

x^4+y^4+(x+y)^4
=(x^2+y^2)^2-2x^2y^2+(x+y)^4
=[(x+y)^2-2xy]^2-2x^2y^2+(x+y)^4
=[(x+y)^2]^2-4xy(x+y)^2+4x^2y^2-2x^2y^2+(x+y)^4
=2(x+y)^4-4xy(x+y)^2+2x^2y^2
=2[(x+y)^4-2xy(x+y)^2+(xy)^2]
=2[(x+y)^2-xy]^2
=2(x^2+xy+y^2)^2.