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a. 3 x 52-- 16:22
= 3 \(\times\)25 - 16 : 4
= 75 - 4
= 71
b. (39x42 --37x42) : 42
= 42 \(\times\)(39 - 37) : 42
= 42 \(\times\)2 : 42
= 84 : 42
= 2
1448 : [119 - (23-6)]
= 1448 : (119 - 17)
= 1448 : 102
= \(\frac{724}{51}\)
a. \(-a-\left(b-a-c\right)=-a-b+a+c=c-b\)
b. \(-\left(a-c\right)-\left(a-b+c\right)=-a-c-a+b-c=b-2a-2c\)
c. \(b-\left(b+a-c\right)=b-b-a+c=c-a\)
d.\(-\left(a-b+c\right)-\left(a+b+c\right)=-a+b-c-a-b-c=-2a-2c=-2\left(a+c\right)\)e. \(\left(a+b\right)-\left(a-b\right)+\left(a-c\right)-\left(a+c\right)=a+b-a+b+a-c-a-c=2b-2c=2\left(b-c\right)\)
f. \(\left(a+b-c\right)+\left(a-b+c\right)-\left(b+c-a\right)-\left(a-b-c\right)=a+b-c+a-b+c-b-c+a-a+b+c=2a\)
a) -a - (b - a - c)
= -a - b + a + c
=[ -a + a] - (b + c)
= 0 - (b + c)
= -(b + c)
d) -(a - b + c) - (a + b + c)
= -a + b - c - a - b - c
= (-a - a) + (b - b) + (c - c)
= (-a - a) + 0 + 0
= -a - a
e) (a + b) - (a - b) + (a - c) - (a + c)
= a + b - a + b + a - c - a - c
= (a - a) - (a + a) + (b + b) - (c - c)
= 0 + 2a + 2b - 0
= 2a + 2b
b) -(a - c) - (a - b + c)
= -a + c - a + b - c
= (-a - a) + (c - c) + b
= [(-a) + (-a)] + 0 + b
= 2(-a) + b
c) b - (b + a - c)
= b - b - a + c
= 0 - a - c
= -a - c
f) (a + b - c) + (a - b + c) - (b + c - a) - (a - b - c)
= 0 - (b + c - a) - (a - b - c)
= 0 - b - c + a - a + b - c
= -b - c + a - a + b - c
= (-b + b) - (c - c) + (a - a)
= 0 - 0 + 0
= 0
a, \(\left(a-b\right)+\left(c-d\right)=\left(a+c\right)-\left(b+d\right)\)
\(a-b+c-d=a+c-b-d\)
\(\Rightarrow VT=VP\left(đpcm\right)\)
b, \(\left(a-b\right)-\left(c-d\right)=\left(a+d\right)-\left(b+c\right)\)
\(a-b-c+d=a+d-b-c\)
\(\Rightarrow VT=VP\left(đpcm\right)\)
c, \(a-\left(b-c\right)=\left(a-b\right)+c=\left(a+c\right)-b\)
\(a-b+c=a-b+c=a+c-b\)
\(\Rightarrowđpcm\)
d, \(\left(a-b\right)-\left(b+c\right)+\left(c-a\right)-\left(a-b-c\right)=-\left(a+b-c\right)\)
\(a-b-b-c+c-a-a+b+c=-a-b+c\)
\(-a-b+c=-a-b+c\)
\(\Rightarrow VT=VP\left(đpcm\right)\)
e, \(-\left(-a+b+c\right)+\left(b+c-1\right)=\left(b-c+6\right)-\left(7-a+b\right)+c\)
\(a-b-c+b+c-1=b-c+6-7+a-b+c\)
\(a-1=-1+a\Rightarrow a-1=a+\left(-1\right)\Rightarrow a-1=a-1\)
\(\Rightarrow VT=VP\left(đpcm\right)\)
-a-b+a+c=-b+c
-a+b-c-a-b-c=-2a-2c
a+b-a-b+a-c-a-c=-2c
-a-c+a-b-c=-2c+b
b-b-a+c=-a+c
a+b-c+a-b+c-b+c-a-a+b+c=2c
a+a+b+c=42
a+b+c+c=52
a+b+b+c=46
vậy c+c+c+c=?
bài giải:
46-42=a + b + b + c - a + a + b + c= b - c =4
52-42=a+b+c+c - a+a+b+c= c-a=10
52-46=a+b+c+c-a+b+b+c=c-b= 6
=> c-b=6 ;c-a=10 ; b-c = 4
a+b+c+c+10+6=c+c+c+c=52+16=68
=> c=17 ; c+c+c+c = 68
a) a(b-c)+c(a-b)=ab-ac+ca-cb=ab-cb=b(a-c)
b) a(b-c)-b(a+c)=ab-ac-ab-bc=-ac-bc=-c(a+b)
c) a(b+c)-b(a-c)=ab+ac-ab+bc=ac+bc=c(a+b)
d) a(b-c)-a(b+d)=ab-ac-ab-ad=-ac-ad=-a(a+d)
\(C=39\cdot42+24\cdot61-39\cdot18\)
\(C=\left(39\cdot42-39\cdot18\right)+24\cdot61\)
\(C=39\cdot\left(42-18\right)+24\cdot61\)
\(C=39\cdot24+24\cdot61\)
\(C=24\cdot\left(39+61\right)\)
\(C=24\cdot100\)
\(C=2400\)