代数 チートシート
−(a±b)=−a∓b
a(b+c)=ab+ac
a(b+c)(d+e)=abd+abe+acd+ace
(a+b)(c+d)=ac+ad+bc+bd
−(−a)=a
0a =0 , a≠0
a1 =a
aa =1
(ab )−1=1ab =ba
(ab )−c=((ab )−1)c=(ba )c
a−1=1a
a−b=1ab
−a−b =ab
−ab =−ab
a−b =−ab
abc =a·cb
bc a =bc·a
1bc =cb
|−a|=|a|
|a|=a , a≥0
|ax|=a|x| , a≥0
1a=1
a1=a
a0=1 , a≠0
0a=0 , a≠0
(ab)n=anbn
aman =am−n , m>n
aman =1an−m , n>m
ab+c=abac
(ab)c=ab·c
abx=(ab)x
(ab )c=acbc
ac·bc=(a·b)c
√1=1
√0=0
n√a=a1n
n√am=amn
√a√a=a
n√an=a, a≥0
n√an=|a|, n is even
n√an=a, n is odd
n√ab=n√an√b, a,b≥0
n√ab =n√an√b , a,b≥0
x2−y2=(x−y)(x+y)
x3+y3=(x+y)(x2−xy+y2)
xn−yn=(x−y)(xn−1+xn−2y+…+xyn−2+yn−1)
xn+yn=(x+y)(xn−1−xn−2y+…−xyn−2+yn−1) n is odd
ax(2n)−b=(√axn+√b)(√axn−√b)
ax(4)−b=(√ax2+√b)(√ax2−√b)
ax(2n)−by(2m)=(√axn+√bym)(√axn−√bym)
ax(4)−by(4)=(√ax2+√by2)(√ax2−√by2)
n!(n+m)! =1(n+1)·(n+2)⋯(n+m)
n!(n−m)! =n·(n−1)⋯(n−m+1),n>m
0!=1
n!=1·2⋯(n−2)·(n−1)·n
log(1)=0
loga(a)=1
loga(xb)=b·loga(x)
logab(x)=1b loga(x)
loga(1x )=−loga(x)
log1a (x)=−loga(x)
loga(b)=ln(b)ln(a)
logx(xn)=n
logx((1x )n)=−n
aloga(b)=b
00=未定義
x0 =未定義
loga(b)=未定義 , a≤0
loga(b)=未定義 , b≤0
log1(a)=未定義
代数
三角関数
