鬼泣4back:因式分解

1.原式=(x^2+2x)^2-18(x^2+2x)+45
=(x^2+2x-3)(x^2+2x-15)
=(x+3)(x-1)(x-3)(x+5)
2.原式=(3x+3y+3z+x-y-z)(3x+3y+3z-x+y+z)
=(4x+2y+2z)(2x+4y+4z)
=4(2x+y+z)(x+2y+2z)
3.题好象错了.如果是(x+y)^2-2x-2y+1
原式=(x+y)^2-2(x+y)+1
=(x+y-1)^2

1)(x^2+2x-18)(x^2+2x)+45
=[X^2+2X]^2-18[X^2+2X]+45
=[X^2+2X-15][X^2+2X-3]
=[X+5][X-3][X+3][X-1]

(2)9（x+y+z）^2-(x-y-z)^2
=[3(X+Y+Z)+(x-y-z)][3(x+y+z)-(x-y-z)]
=[4x+2y+2z][2x+4y+4z]

(3)(x+y)^2-2x-2y+2
=[x+y]^2-2[x+y]+2
=[x+y-1]^2+1

第一题给你做了，第三题可能数字有错。

把多项式看成一个整体
例如
第一题把x^2+2x看成一个整体X
则可以解得
(x^2+2x-18)(x^2+2x)+45=(x^2+2x)^2-18(x^2+2x)+45
=(x^2+2x-3)(x^2+2x-15)=(x-1)(x+3)(x-3)(x+5)
第二题
9(x+y+z)^2-(x-y-z)^2=(3x+3y+3z)^2-(x-y-z)^2
=(3x+3y+3z+x-y-z)(3x+3y+3z-x+y+z)
=(4x+2y+2z)(2x+4y+4z)=4(2x+y+z)(x+2y+2z)
第三题
(x+y)^2-2x-2y+2=(x+y)^2-2(x+y)+1+1
=(x+y+1)^2+1
哦,累死了,可能会出现差错,望后来者居上.

1,把x^2+2x看作整体或者用t代换
2,平方差公式,很简单的.
3,把x+y看作整体或者代换

因式分解——十字相乘法 =