问几个数学分解因式的题

来源:百度知道 编辑:UC知道 时间:2024/06/17 06:06:44
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) , (x+y)^2-16(x-y)^2 , 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 ,就这几个^2是平方^3是立方
步骤 多多少少写上一步

1.7x^2-63=7(x^2-9)=7(x+3)(x-3)
2.a^3-a=a(a^2-1)=a(a+1)(a-1)
3.y^2-9(x+y)^2=[y+3(x+y)][y-3(x+y)]=(3x+4y)(-3x-2y)
4. a(x-y)-b(y-x)+c(x-y)=(a+b+c)(x-y)
5. x(m+n)-y(n+m)+(m+n) =(x-y+1)(m+n)
6.(x+y)^2-16(x-y)^2=[(x+y)+4(x-y)][(x+y)-4(x-y)]=(5x-3y)(-3x+5y)
7.a^2(a-b)^2-b^2(a+b)^2 [a(a-b)+b(a+b)][a(a-b)-b(a+b)]=(a^2+b^2)(a^2-2ab-b^2)
8.(x+y+z)^2-(x-y-z)^2=2x(2y+2z)=4x(y+z)
9.(x+y)^2-14(x+y)+49=[(x+y)-7]^2=(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+b)(a-b).
原式=(a+b+c)(x-y).
原式=(m+n)(x-y+1).
原式=(x+y+4x-4y)(x+y-4x+4y)=(5x-3y)(5y-3x).
原式=(a^2-ab+ab+b^2)(a^2-ab-ab-b^2)=(a^2+b^2)(a^2-2ab-b^2).
(x+y+z)^2-(x-y-z)^2=2xy+2yz+2xz-(-2xy-2xz+2yz)=4xy+4xz=4x(y+z).
(x+y)^2-14(x+y)+49=(x+y-7)^2.

作业好好写