Question

4m的3次方乘以n-16mn的3次方的分解因式

Answer 1

上面的怎么感觉越分解越难了啊,应该=4m^3*n^3(1-16m)^3=4[mn(1-16m)]^3

追问的答案是4m^3n-16mn^3=4mn(m^2-n^2)=4mn(m-n)(m+n)

Answer 2

(4m)^3x(n-16mn)^3=64m^3x(n-16mn)^2x(n-16mn)
=64m^3x(n^2+16^2m^2n^2-32mn^2)(n-16mn)
=64m^3x(n^3+16^2m^2n^3-32mn^3-16mn^3-16^3m^3n^3+32x16m^2n^3)
=64^3x(n^3-48mn^3-16^3m^3n^3+48x16m^2n^3)
=64m^3n^3-3072mn^3-262144m^6n^3+49152m^5n^3

追问

4m^3n-16mn^3的分解因式

追答

=4mn(m^2-4n^2)
=4mn(m+n)(m-n)