a/ - b - (b - a + c)
= - b - b + a -c
b/ - (a - b + c) - (c - a)
= - a + b - c - c + a
c/ b - (b + a - c)
= b - b - a + c
d/ a - (- b + a - c)
= a + b - a + c
a) -b - ( b - a + c )
= -b - b + a - c
=-2b + a - c
b) - ( a- b + c ) - ( c - a )
= - a + b -c -c + a
= b-2c
c) b - ( b + a - c )
= b - b - a + c
= -a + c
d) a - ( -b + a - c )
= a + b - a + c
= b + c
Rút gọn các biểu thức sau :
a) \(A=\left(a-b\right)+\left(a+b-c\right)-\left(a-b-c\right)\)
b) \(B=\left(a-b\right)-\left(b-c\right)+\left(c-a\right)-\left(a-b-c\right)\)
c) \(C=\left(-a+b+c\right)-\left(a-b+c\right)-\left(-a+b-c\right)\)
Chứng minh đẳng thức:
a) \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)=\left(a-c\right)\left(d-b\right)\)
b) \(\left(a-c\right)\left(b+d\right)-\left(a-d\right)\left(b+c\right)=\left(a+b\right)\left(d-c\right)\)
Chứng minh các đẳng thức sau:
a) \(\left(a+b\right)-\left(-a+b-c\right)+\left(c-a-b\right)=a-b+2c\)+ 2c
b) \(a\left(b-c\right)-a\left(b+d\right)=-a\left(c+d\right)\)
Đơn giản biểu thức:
\(a>\left(a+h\right)-\left(-c+a+b\right)\)
\(b>-\left(x+y\right)+\left(-z+x+y\right)\)
Chứng minh đẳng thức
a) \(\left(x-y\right)-\left(x-z\right)=\left(z+x\right)-\left(y+x\right)\)
b) \(\left(x-y+z\right)-\left(y+z-x\right)-\left(x-y\right)=\left(z-y\right)-\left(z-x\right)\)
c) \(a\left(b+c\right)-b\left(a-c\right)=\left(a+b\right)c\)
d) \(a\left(b-c\right)-a\left(b+d\right)=-a\left(c+d\right)\)
e) \(\left(a+b\right)\left(c+d\right)-\left(a+d\right)\left(b+c\right)=\left(a-c\right)\left(d-b\right)\)
f) \(\left(a-c\right)\left(b+d\right)-\left(a-d\right)\left(b+c\right)=\left(a+b\right)\left(d-c\right)\)
Chứng minh đẳng thức
\(\left(a-c\right)\left(b+d\right)-\left(a-d\right)\left(b+c\right)=\left(a+b\right)\left(d-c\right)\)
Rút gọn biểu thức :
\(A=\left(a+b-c\right)+\left(a-b\right)-\left(a-b\right)-\left(a-b-c\right)\)
CMR
\(a,\left(a-b\right)+\left(c-d\right)=\left(a+c\right)-\left(b+d\right)\)
\(b,\left(a-b\right)-\left(c-d\right)=\left(a+d\right)-\left(b+c\right)\)
Bài 1 :Chứng tỏ rằng:
\(\left(a-b\right)-\left(b+c\right)+\left(c-a\right)-\left(a-b-c\right)=\)\(-\left(a+b-c\right)\)
Bài 2 : Cho \(a,b,c,d\in N\) và \(a\ne0\).Chứng tỏ rằng biếu thức P luôn âm , biết rằng ;
\(P=a.\left(b-a\right)-b.\left(a-c\right)-bc\)
