Question

八下的一些分解因式题（在线等）急急急

①4（x+y+z)²-9（x-y-z)².
②9（x+y)²+12（x+y）+4.
③（x²+9）²-36x²
④（x-y)(x-y-12)+36.
⑤18m²-m4（m的四次方）-81
④（x-y)(x-y-12)+36这道题不太理解，能在详细一些不？？

Answer 1

①4（x+y+z)^2-9（x-y-z)^2 用平方差公式
=[2(x+y+z)]^2-[3(x-y-z)]^2
=[2(x+y+z)+3(x-y-z)][2(x+y+z)-3(x-y-z)]
=(5x-y-z)(5y+5z-x)
②9（x+y)^2+12（x+y）+4 用完全平方公式
=[3(x+y)]^2+2*2*3(x+y)+2^2
=[3(x+y)+2]^2
③（x^2+9)^2-36x^2 用平方差公式
=[x^2+9+6x][x^2+9-6x] 各项再用完全平方公式
=(x+3)^2(x-3)^2
④（x-y)(x-y-12)+36
=(x-y)^2-12(x-y)+36 用完全平方公式
=(x-y-6)^2
⑤18m^2-m^4-81
=-(m^4-18m^2+81) 完全平方公式
=-(m^2-9)^2 再用平方差公式
=-(m+3)^2(m-3)^2

Answer 2

1. =[2(x+y+z)+3(x-y-z)][2(x+y+z)-3(x-y-z)]
=(5x-y-z)(-x+5y+5z)
2. =[3(x+y)+2]²
3. =(x²+9+6x)(x²+9-6x)
=(x+3)²(x-3)²
4. =(x-y)²-12(x-y)+36
=(x-y-6)²
5. =-(m²-9)²

Answer 3

1. =4[(x+y)^2+2(x+y)z+z^2]-9x^2-9y^2-9z^2+18xy+18xz-18yz=-5(x^2+y^2+z^2)+26xy+26xz-10yz
2. =9(x^2+2xy+y^2)+12(x+y)+4 或={3(x+y)+2}^2 ^2代表 平方
3. =[(x^2+9)-6x][x^2+9+6x]=[(x-3)^2][(x+3)^2]=(x-3)^2 *(x+3)^2
4. =(x-y)^2-12(x-y)+36=[(x-y)-6]^2
5.=18m^2-m^4-81=-[(m^2)^2-2*9m-9^2]=(m^2-9)^2 或=（m平方减去9）的平方