作业帮已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值(m+n)^2-n^24a^2-(b+c)^2169(a-b)^2-196(a+b)^2(a+b+c)^2-(a+b-c)^24(2p+3q)^2-(3p-q)^21-a^42ab^3-2ab3a-3ay^4(2x+1)(x-1)-(x+1)(x-2)-10
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 15:49:47
已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值(m+n)^2-n^24a^2-(b+c)^2169(a-b)^2-196(a+b)^2(a+b+c)^2-(a+b-c)^24(2p+3q)^2-(3p-q)^21-a^42ab^3-2ab3a-3ay^4(2x+1)(x-1)-(x+1)(x-2)-10
已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值
(m+n)^2-n^2
4a^2-(b+c)^2
169(a-b)^2-196(a+b)^2
(a+b+c)^2-(a+b-c)^2
4(2p+3q)^2-(3p-q)^2
1-a^4
2ab^3-2ab
3a-3ay^4
(2x+1)(x-1)-(x+1)(x-2)-10
已知4m+n=90,2m-3n=10,求(m+2n)^2-(3m-n)^2的值(m+n)^2-n^24a^2-(b+c)^2169(a-b)^2-196(a+b)^2(a+b+c)^2-(a+b-c)^24(2p+3q)^2-(3p-q)^21-a^42ab^3-2ab3a-3ay^4(2x+1)(x-1)-(x+1)(x-2)-10
(m+2n)^2-(3m-n)^2
=(m+2n+3m-n)(m+2n-3m+n)
=(4m+n)(-2m+3n)
=-(4m+n)(2m-3n)
=-90×10
=-900
(m+n)^2-n^2=(m+n+n)(m+n-n)=m(m+2n)
4a^2-(b+c)^2=(2a+b+c)(2a-b-c)
169(a-b)^2-196(a+b)^2
=(13a-13b+14a+14b)(13a-13b-14a-14b)
=(27a+b)(-a-27b)
=-(27a+b)(a+27b)
(a+b+c)^2-(a+b-c)^2=(a+b+c+a+b-c)(a+b+c-a-b+c)=(2a+2b)(2c)=4c(a+b)
4(2p+3q)^2-(3p-q)^2=(4p+6q)²-(3p-q)²=(4p+6q+3p-q)(4p+6q-3p+q)=(7p+5q)(p+7q)
1-a^4=(1+a²)(1-a²)=(1+a²)(1+a)(1-a)
2ab^3-2ab=2ab(b²-1)=2ab(b+1)(b-1)
3a-3ay^4=3a(1-y^4)=3a(1+y²)(1-y²)=3a(1+y²)(1+y)(1-y)
(2x+1)(x-1)-(x+1)(x-2)-10=(2x²-x-1)-(x²-x-2)-10=x²-9=(x+3)(x-3)
这是因式分解题？原式直接求出m,n带入计算。