Question

把多相式x的三次方减6x的2次方y加12xy的2次方减8y的3次方加1写成2个整式的和,使其中一个不含字母x

Answer 1

x^3-6x^2y+12xy^2-8y^3+1

=(x^3-8y^3)-6x^2y+12xy^2+1

=(x-2y)(x^2+4y^2+2xy)-6xy(x-2y)+1

=(x-2y)(x^2+4y^2+2xy-6xy)+1

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

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

=(x-2y)^3+1