因式分解-9m^2-4n^2+12mn=________
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因式分解-9m^2-4n^2+12mn=________
4x^2-16;a^4(x-y)+b^4(y-x);(a^2+1)^2-4a(a^2+1)+4a^2
4x^2-16;a^4(x-y)+b^4(y-x);(a^2+1)^2-4a(a^2+1)+4a^2
![因式分解-9m^2-4n^2+12mn=________](/uploads/image/z/18977057-17-7.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3-9m%5E2-4n%5E2%2B12mn%3D________)
1、4x^2-16=4(x^2-2^2)=4(x-2)(x+2)
2、a^4(x-y)+b^4(y-x)=(x-y)(a^4-b^4)=(x-y)(a^2-b^2)(a^2+b^2)=(x-y)(a+b)(a-b)(a^2+b^2)
3、(a^2+1)^2-4a(a^2+1)+4a^2=(a^2+1)^2-4a(a^2+1)+(2a)^2=(a^2+1-2a)(a^2+1+2a)=(a+1)(a-1)(a+1)(a+1)=(a-1)(a+1)^3
2、a^4(x-y)+b^4(y-x)=(x-y)(a^4-b^4)=(x-y)(a^2-b^2)(a^2+b^2)=(x-y)(a+b)(a-b)(a^2+b^2)
3、(a^2+1)^2-4a(a^2+1)+4a^2=(a^2+1)^2-4a(a^2+1)+(2a)^2=(a^2+1-2a)(a^2+1+2a)=(a+1)(a-1)(a+1)(a+1)=(a-1)(a+1)^3