Question

求求大哥们帮我做下下列十道题吧， 用因式分解做， 要过程， 谢谢啦！我的分都给他100分

121x^4-4y^2
4/25a^2-X^2y^2
(m+n)^2-n^2
4(2p+3q)^2-(3p-q)^2
81a^4-2y^2
8y^4-2y^2
3ax^2-3ay^4
m^4-1
12x^2-3y^2
(2x+y)^2-(x+2y)^2

Answer 1

这10道题都属于同一个类型，都是x^2-y^2=(x+y)(x-y)的变形。
1.121x^4-4y^2=(11x^2)^2-(2y)^2=(11x^2+2y)(11x^2-2y)
2.4/25a^2-X^2y^2=(2/5a)^2-(xy)^2=(2/5a+xy)(2/5a-xy)
3.(m+n)^2-n^2=(m+n+n)(m+n-n)=m(m+2n)
4.4(2p+3q)^2-(3p-q)^2=(2(2p+3q))^2-(3p-q)^2=(4p+6q+3p-q)(4p+6q-3p+q)=(7p+5q)(p+7q)
5.81a^4-2y^2=(9a^2)^2-（根号2y)^2=(9a^2+根号2y)(9a^2-根号2y)
6.8y^4-2y^2=2y^2((2y)^2-1)=2(2y+1)(2y-1)
7.3ax^2-3ay^4=3a(x^2-(y^2)^2)=3a(x+y^2)(x-y^2)
8.m^4-1=(m^2)^2-1=(m^2+1)(m^2-1)=(m^2+1)(m+1)(m-1)
9.12x^2-3y^2=3((2x)^2-y^2)=3(2x+y)(2x-y)
10.(2x+y)^2-(x+2y)^2=(2x+y+x+2y)(2x+y-x-2y)=(3x+3y)(x-y)=3(x+y)(x-y)