(㎡-4m)(㎡-4m-2)-15;要详细的步骤,
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(㎡-4m)(㎡-4m-2)-15;要详细的步骤,
(㎡-4m)(㎡-4m-2)-15;要详细的步骤,
(㎡-4m)(㎡-4m-2)-15;要详细的步骤,
整理观察嘛先,发现都有一个m^2 - 4m的因子,所以呢可以将m^2 - 4m看作一个整体,或者令 y = m^2 - 4m也成
所以:(m^2 - 4m)(m^2 - 4m - 2) = (m^2 - 4m)^2 - 2(m^2 - 4m) - 15
又因为 -15 = -5 * 3
所以 (m^2 - 4m)^2 - 2(m^2 - 4m) - 15 = (m^2 - 4m + 3)(m^2 - 4m - 5)
又因为 (m^2 - 4m + 3) = (m - 3)(m - 1)
且 (m^2 - 4m - 5) = (m - 5)(m + 1)
所以 (m^2 - 4m + 3)(m^2 - 4m - 5) = (m - 3)(m - 1)(m - 5)(m + 1)
所以最后的结果就是:
(m - 3)(m - 1)(m - 5)(m + 1)
用换元法，令㎡-4m＝t
t(t-5)-15=0
t^2-5t-15=0
(t-5)(t+3)=0
t=5,t=-3
当t=5时
㎡-4m=5
(m-5)(m+1)=0
m=5,m=-1
当t=-3时
㎡-4m=-3
(m-1)(m-3)=0
m=1,m=3
所以
m=5
m=-1
m=1
m=3
x
可以用换元法分解因式，把m平方-4m设成y，则变成y（y-2)-15=y平方-2y-15
分解得（y+3)(y-5) 再还原（m平方-4m+3)(m平方-4m-5)
：(㎡-4m)(㎡-4m-2)-15
=(m^2-4m)^2-2(m^2-4m)-15
=(m^2-4m-5)(m^2-4m+3)
=(m-5)(m+1)(m-1)(m-3)