x+2y+4y^2/x-y+4x^y/4y^2-x^2

x+2y+4y^2/x-y+4x^y/4y^2-x^2
x+2y+4y^2/x-y+4x^y/4y^2-x^2

x+2y+4y^2/x-y+4x^y/4y^2-x^2
“4y^2/x-y”应该是“4y^2/x-2y”吧
x+2y+4y^2/x-2y+4x^2y/4y^2-x^2
=(x+2y)+4y^2/(x-2y)+4x^2y/(2y-x)(2y+x)
=(x+2y)+[4y^2(x+2y)-4x^2y]/(x-2y)(2y+x)
=(x+2y)+4y(2y-x)(x+y)/(x-2y)(2y+x)
=(x+2y)-4y(x+y)/(x+2y)
=[(x+2y)^2-4y(x+y)]/(x+2y)
=x^2/(x+2y)

1. （x+y)^2-16(x-y)^2=（x+y)^2-(4x-4y)^2=（x+y+4x-4y)(x+y-4x+4y)=(5x-3y)(5y-3x)
2. 49(x-y)^2-16(x+y)^2=(7x-7y)^2-(4x+4y)^2=(7x-7y+4x+4y)(7x-7y-4x-4y)=(11x-3y)(3x-11y)
3. 4-12(a+b)+9(a+b)^2=[2-...

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1. （x+y)^2-16(x-y)^2=（x+y)^2-(4x-4y)^2=（x+y+4x-4y)(x+y-4x+4y)=(5x-3y)(5y-3x)
2. 49(x-y)^2-16(x+y)^2=(7x-7y)^2-(4x+4y)^2=(7x-7y+4x+4y)(7x-7y-4x-4y)=(11x-3y)(3x-11y)
3. 4-12(a+b)+9(a+b)^2=[2-3(a+b)]^2=(2-3a-3b)^2
4. 5x^3-20xy^2=5x(x^2-4y^2)=5x(x+2y^2)(x-2y^2)
5. x^2-2x(y+z)+(y+z)^2 =(x-y-z)^2
6. 4ab^2-4a^2b-b^3=-b(-4ab+4a^2+b^2)=-b(2a-b)^2
7. x^4-y^4=(x^2+y^2)(x^2-y^2)=(x^2+y^2)(x+y)(x-y)
8. (a^2+4)^2-16a^2 =(a^2+4+4a)(a^2+4-4a)=(a+2)^2(a-2)^2
9. x^4-8x^2y^2+16y^4=(x^2-4y^2)^2=(x+2y)^2(x-2y)^2
10. a(x-y)+b(y-x)-c(x-y) =(a-b-c)(x-y)
11. x(a+b)+y(b+a)-(a+b)=(x+y-1)(a+b)
12. x^2-2xy^2+y^3题目打错？若是 x^2y-2xy^2+y^3=y(x-y)^2
13. 2a^2+6a+9/2=2（a+3/2)^2

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