中科新闻网神雕侠侣 搜狐:把下列各式分解因式
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2.4m(m-n)+4n(n-m)
3.16x^2-64
4.-4a^2+24a-36
5.x^4-2x^2+1
6.(a^2+4)^2-16a^2
7.2x^3(a-1)+8x(1-a)
8.(x^2-3)^2-12(x^2-3)+36 要写出过程。
1.(2a+4a^2)-4a^2 =2a+4a^2-4a^2=2a
2.4m(m-n)+4n(n-m) =4m^2-4mn+4n^2-4mn=4(m^2-2mn+n^2)=4(m-n)^2
3.16x^2-64 =16(x^2-4)=16(x+2)(x-2)
4.-4a^2+24a-36 =-4(a^2-6a+9)=-4(a-3)^2
5.x^4-2x^2+1 =(x^2-1)^2=(x-1)(x+1)(x-1)(x+1)=(x-1)^2(x+1)^2
6.(a^2+4)^2-16a^2 =a^4+8a^2+16-16a^2=a^4-8a^2+16=(a^2-4)^2=(a+2)(a-2)(a+2)(a-2)=(a+2)^2(a-2)^2
7.2x^3(a-1)+8x(1-a) =2ax^3-2x^3+8x-8ax=2x(ax^2-x^2+4-4a)=2x[x^2(a-1)-4(a-1)]=2x(a-1)(x^2-4)=2x(a-1)(x-2)(x+2)
8.(x^2-3)^2-12(x^2-3)+36 =[(x^2-3)-6]^2=(x^2-9)^2=(x+3)(x-3)(x+3)(x-3)=(x=3)^2(x-3)^2
1.化简=2a
2.同时提出(m-n)=4(m-n)^2
3.=(4x+8)(4x-8)
4.=-(2a-6)^2
5.=(x^2-1)^2
6.=(a^2+4+4a)(a^2+4-4a)
=(a+2)^2(a-2)^2
=(a+2)(a+2)(a-2)(a-2)
7.先提出2x(a-1)所以=2x(a-1)(x+2)(x-2)
8.将(x^2-3)看作一个整体,所以=(x^2-3-6)^2
=(x+3)(x+3)(x-3)(x-3)