问几个分解因式题

来源:百度知道 编辑:UC知道 时间:2024/06/03 22:55:52
7x^2-63 , a^3-a , 3a^2-3b^2 , y^2-9(x+y)^2 , a(x-y)-b(y-x)+c(x-y) , x(m+n)y(n+m)+(m+n) , a^2(a-b)^2-b^2(a+b)^2 , (x+y+z)^2-(x-y-z)^2 , (x+y)^2-14(x+y)+49 速度了,步骤写出来啊,不写的没分啊,急啊,速度了

7x^2-63=7(x^2-3^2)=7(x+3)(x-3)
a^3-a=a(a^2-1^2)=a(a+1)(a-1)
3a^2-3b^2=3(a^2-b^2)=3(a+b)(a-b)
y^2-9(x+y)^2=[y+3(x+y)][y-3(x+y)]=-(3x+4y)(3x+2y)
a(x-y)-b(y-x)+c(x-y)=(x-y)[a-(-b)+c]=(x-y)(a+b+c)
x(m+n)y(n+m)+(m+n)=这个题目你复核一下
a^2(a-b)^2-b^2(a+b)^2=[a(a-b)+b(a+b)][a(a-b)-b(a+b)]=(a²+b²)(a²-2ab-b²)
(x+y+z)^2-(x-y-z)^2=[(x+y+z)+(x-y-z)][(x+y+z)-(x-y-z)]=2x(2y+2z)=4x(y+z)
(x+y)^2-14(x+y)+49=(x+y)^2-2*7(x+y)+7²=(x+y-7)²

7x^2-63=7(x^2-9)=7(x+3)(x-3)

a^3-a=a(a^2-1)=a(a+1)(a-1)

3a^2-3b^2=3(a^2-b^2)=3(a+b)(a-b)

y^2-9(x+y)^2=(y+3(x+y))(y-3(x+y))=-(3x+4y)(3x+2y)

a(x-y)-b(y-x)+c(x-y)=(x-y)(a+b+c)

x(m+n)+y(n+m)+(m+n)=(m+n)(x+y+1)

a^2(a-b)^2-b^2(a+b)^2=(a(a-b))^2-(b(a+b))^2
=(a(a-b)+b(a+b))(a(a-b)-b(a+b))
=(a^2+b^2)(a^2-2ab-b^2)

(x+y+z)^2-(x-y-z)^2=((x+y+z)+(x-y-z))((x+y+z)-(x-y-z))
=4x(y+z)

(x+y)^2-14(x+y)+49=((x+y)-7)^2=(x