13问答网 > 因式分解:1、m^4+m^2-20 2、（m-n)^2-3(m-n)-40 3、(x-y)^2-4(x-y+15) 4、x^2(x^2-y^2)-72y^4

因式分解:1、m^4+m^2-20 2、（m-n)^2-3(m-n)-40 3、(x-y)^2-4(x-y+15) 4、x^2(x^2-y^2)-72y^4

^是平方的意思。求大神帮助啊啊。跪下了。。

2024-11-22 15:47:28

推荐回答（2个）

回答1：

1、m^4+m^2-20
=(m-4)(m+5）

2、（m-n)^2-3(m-n)-40
=（m-n+5)(m-n-8)

3、(x-y)^2-4(x-y+15)
=(x-y)^2-4(x-y)-60
=(x-y+6)(x-y-10)

4、x^2(x^2-y^2)-72y^4
=x^4-x²y²-72y^4
=(x²+8y²)(x²-9y²)
=(x²+8y²)(x+3y)(x-3y)

回答2：

1、m^4+m^2-20
=(m²+5)(m²-4)
=(m²+5)(m+2)(m-2)

2、（m-n)^2-3(m-n)-40
=(m-n-8)(m-n+5)

3、(x-y)^2-4(x-y+15)
=(x-y)²-4(x-y)-60
=(x-y-10)(x-y+6)

4、x^2(x^2-y^2)-72y^4
=x^4-x²y²-72y^4
=(x²-9y²)(x²+8y²)
=(x+3y)(x-3y)(x²+8y²)