m²（m²+3n）²+4n³因式分解

先换元,设m^2=a
原式=a(a+3n)^2+4n^3
=a^3+6a^2n+9an^2+4n^3
=a^3+3a^2n+3an^2+n^3+3a^2n+6an^2+3n^3
=(a+n)^3+3n(a^2+2an+n^2)
=(a+n)^3+3n(a+n)^2
=(a+n)^2(a+n+3n)
将m^2=a代入
原式=(m^2+n)^2(m^2+4n)

(m2+n)2 X (m2+4n)

先换元，再十字相乘

m²(m²+3n)²+4n³=(m²+n)²(m²+4n)