Question

2(m^2+n^2)^2-8m^2n^2 因式分解

Answer 1

完全平方公式（a-b）²=a²+b²-2ab
设a=m²,b=n²
代入得（m²-n²）²=(m²)²+(n²)²-2m²n² {①式}

2（m²+n²）²-8m²n² 利用完全平方公式化简
=2(m^4 + n^4 +2m²n²) -8m²n² 去掉括号
=2m^4 +2n^4 +4m²n²-8m²n² 化简
=2m^4 +2n^4 -4m²n²
=2(m^4 +n^4 -2m²n²) 完全平方公式的倒用,将m^4看成m²的平方
=2[(m²)²+(n²)²-2m²n²] 根据①式
=2(m²-n²)²

Answer 2

2(m^2+n^2)^2-8m^2n^2
=2[(m^2+n^2)^2-(2mn)^2]
=2(m^2+n^2+2mn)(m^2+n^2-2mn)
=2[(m+n)(m-n)]^2

Answer 3

2(m^2-n^2)^2 显然啊~

Answer 4

2(m^2-n^2)^2