Thu gọn biểu thức − c + a − b + d − a − c − b + b − a − d + b − a với a , b , c , d ∈ ℤ ta được biểu thức
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a) A = ( a+ b – c + d ) – ( - a – b + c – d )
= a+ b – c + d + a + b - c + d
= 2a + 2b + 2d – 2c
b) B = ( a+ b – c ) + ( a – b ) – ( a – b - c )
= a+ b – c + a – b – a + b + c
= a + b
A = ( a+ b – c + d ) – ( - a – b + c – d )
= a+ b – c + d + a + b - c + d
= 2a + 2b + 2d – 2c
Bài làm
\(a\left(b-c-d\right)-b\left(c+a\right)=ab-ac-ad-bc-ba\)
\(=-ac-ad-bc\)
a ( b - c - d ) - b ( c + a )
=a.b-a.c-a.d-b.c-b.a
= -a.c-c.d-b.c
a) \(\left(a-b-d\right)+\left(b-a-d\right)=a-b-d+b-a-d\)
\(=\left(a-a\right)-\left(b-b\right)-\left(d+d\right)\)
\(=0-2d\)
\(=-2d\)
b) \(-\left(a-b+c\right)-\left(a-b-c\right)=-a+b-c-a+b+c\)
\(=\left(-a-a\right)+\left(b+b\right)-\left(c-c\right)\)
\(=-2a+2b\)
c) \(\left(c-a+d\right)+\left(a-b-d\right)=c-a+d+a-b-d\)
\(=c-\left(a-a\right)+\left(d-d\right)-b\)
\(=c-b\)
a ) \(\left(a-b-d\right)+\left(b-a-d\right)=a-b-d+b-a-d=-2d\)
b ) \(-\left(a-b+c\right)-\left(a-b-c\right)=-a+b-c-a+b+c=-2a+2b=2\left(-a+b\right)\)
c ) \(\left(c-a+d\right)+\left(a-b-d\right)=c-a+d+a-b-d=c-b\)
=a+c+d+c-b-d+b-d+c-a
=(a-a)+(b-b)+(c+c+c)+(d-d-d)
=0+0+3c-d
=3c-d
-(a-c-d)-(-c+b+d)+(b-d+c-a)
=-a+c+d+c+b+d+b-d+c-a
=(-a-a)+(c+c+c)+(d+d-d)+(b+b)
=-2a+3c+d+2b
Vay = -2a+3c+d+2b
a) ( a + b + c ) - ( a - b - c )
= ( a + b + c ) - a + b + c
= a + ( - a ) + b + c + b + c
= 0 + b + c + b + c
= ( b + c ) x 2
b) ( a + b - c ) + ( a - b ) - ( a - b - c )
= ( a + b - c ) + a - b - a + b + c
= [ a + a + ( -a ) ] + [ b + ( -b ) + b ] + [ ( -c ) + c ]
= a + b + 0
= a + b
c) - ( a - b - c ) + ( -a + b - c ) - ( -a + b + c )
= ( -a ) + b + c + ( -a ) + b - c + a - b - c
= [ ( -a ) + ( -a ) + a ] + [ b + b + ( -b ) ] + [ c + ( -c ) + ( -c ) ]
= ( -a ) + b + ( -c )
a , ( a + b + c ) - ( a - b - c )
= a + b + c - a + b + c
= ( a - a ) b + b + c + c
= 0 + b + b + c + c
= 0 + 2b + 2c
= 0 + 2(b + c )
= 2(b+c)
b , ( a + b - c ) + ( a - b ) - ( a - b - c )
= a + b - c + a - b - a + b + c
= ( a - a ) + b + b + ( - c + c )
= 0 + b + b + 0
= 2b
c , - ( a - b - c ) + ( - a + b - c ) - ( - a + b + c )
= - a + b + c - a + b - c + a - b - c
= ( - a + a ) + ( b - b ) + ( c - c ) + a + b
= 0 + 0 + 0 + a + b= a + b
0