Question

m2(m+n)2-n2(m-n)2,分解因式，谢谢！

Answer 1

m2(m+n)2-n2(m-n)2
=[m(m+n)+n(m-n)][m(m+n)-n(m-n)]
=(m2+mn+mn-n2)(m2+mn-mn+n2)
=(m2+2mn-n2)(m2+n2)

Answer 2

m^2(m+n)^2-n^2(m-n)^2
=[m(m+n)-n(m-n)][m(m+n)+n(m-n)]
=(m^2+mn-mn+n^2)(m^2+mn+mn-n^2)
=(m^2+n^2)(m^2+2mn-n^2)

Answer 3

m2(m+n)2-n2(m-n)2
=m²(m+n)²-n²(m-n)²
=[m(m+n)-n(m-n)][m(m+mn)+n(m-n)]
=(m²+mn-mn+n²)(m²+mn+mn-n²)
=(m²+n²)(m²+2mn-n²)

Answer 4

m2(m+n)2-n2(m-n)2
=[m(m+n)+n(m-n)][m(m+n)-n(m-n)]
=(m²+mn+mn-n²)(m²+mn-mn+n²)
=(m²+2mn-n²)(m²+n²)

Answer 5

=[m(m+n)+n(m-n)][m(m+n)-n(m-n)]
=(m^2+2mn-n^2)(m^2+n^2)