因式分解(3m+2n)²-4(m-n)²

因式分解(3m+2n)²-4(m-n)²
因式分解(3m+2n)²-4(m-n)²

因式分解(3m+2n)²-4(m-n)²
(3m+2n)²-4(m-n)²
=(3m+2n)²-2²(m-n)²
=(3m+2n)²-(2m-2n)²
=(3m+2n+2m-2n)(3m+2n-2m+2n)
=5m(m+4n)

(3m+2n)²-4(m-n)²=(3m+2n)²-[2(m-n)]²
=(3m+2n)²-(2m-2n)²
=[(3m+2n)+(2m-2n)][(3m+2n)-(2m-2n)]
=5m(m+4n)

　　先全部乘开
　　的=9m²+12mn+4n²-4m²+8mn-4n².............................化简
　　 =5m²+20mn.....................................因式分解
　　 =5m(m+4n)