Question

因式分解

1.m^4-5m^2+4
2.4(x+y)^3-24(x+y)^2+36(x+y)
3.a^3b-12a^2b^2-32ab^3
4.(m+n)^2+4(m^2-n^2)+12(m-n)^2

Answer 1

1.m^4-5m^2+4
=（m^2-1)(m^2-4)
=（m-1)（m+1)（m-2)(m+2)
2.4(x+y)^3-24(x+y)^2+36(x+y)

=4(x+y)[(x+y)^2-6(x+y)^2+9]
=4(x+y)(x+y-3)^2
3.a^3b-12a^2b^2-32ab^3
=ab(a^2-12ab-32b^2)
题目应是
.a^3b-12a^2b^2+32ab^3
=ab(a^2-12ab+32b^2)
=ab(a-4b)(a-8b)
4.(m+n)^2+4(m^2-n^2)+12(m-n)^2
=m^2+2mn+n^2+4m^2-4n^2+12m^2-24mn+12n^2
=17m^2-22mn+9n^2
题目应是
(m+n)^2+4(m^2-n^2)-12(m-n)^2
=[(m+n)+6(m-n)][(m+n)-2(m-n)]
=(7m-5n)(-m+3n)

追问

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

追答

3(2a+3b)^2-(2a+3b)(3a+2b)-2(3a+2b)^2
=[3(2a+3b)+2(3a+2b)][(2a+3b)-(3a+2b)]
=[(6a+9b)+(6a+4b)][(2a+3b)-(3a+2b)]
=(12a+13b)(-a+b)

Answer 2

1、2（2m-5m+2）=2(-3m+2)
2、12(x+y)(1-4+3)=0
3、3ab(1-16-32)=-141ab
4、2m+2n+8m-8n+24m-24n=34m-30n=2(17m-15n)