Question

4xy+1-4x^2-y^2= x^6-y^6-2x^3+1= x^4+64= x^3-4xy^2-2x^2y+8y^3

Answer 1

我高中数学老师、

应该是这样没错

4xy+1-4x^2-y^2=1-(4x^2-4xy+y^2)=1-(2x-y)^2=(1+2x-y)(1+y-2x)

x^6-y^6-2x^3+1= x^6-x^3-x^3+1-y^6=x^3(x^3-1)-(x^3-1)-y^6=(x^3-1)^2-y^6

=(x^3-1-y^3)(x^3-1+y^3)

x^4+64=x^4+16x^2+64-16x^2=(x^4+16x^2+64)-16x^2=(x^2+8)^2-16x^2=

(x^2+8-4x)(x^2+8+4x)

x^3-4xy^2-2x^2y+8y^3=(x^3+8y^3)-2xy(2y+x)=(x+2y)(x^2-2xy+4y^2)-2xy(x+2y)=(x+2y)(x^2-4xy+4y^2)=(x+2y)(x-2y)^2