Question

Chứng tỏ:

1. (a-b+c) - (a+c) = -b

2. (a+b) - (b-a) + c = 2a + c

3. -(a+b-c) + (a-b-c)= -2b

4. a(b+c) - a(b+d) = a(c-d)

5. a(b-c) + a(d+c) = a(b+d)

Answer 1

1. ( a - b + c ) - ( a + c )
=> a - b + c - a - c
=> ( a - a ) - b + ( c - c )
=> 0 - b + 0
=> -b ( đpcm ).

Answer 2

2. ( a + b ) - ( b - a ) + c
=> a + b - b + a + c
=> ( a + a ) + ( b - b ) + c
=> 2a + c ( đpcm )

Answer 3

3. -( a + b - c ) + ( a - b - c )
=> ( a - b - c ) - ( a + b - c )
=> a - b - c - a - b + c
=> ( a - a ) - ( b + b ) - ( c - c )
=> 0 - 2b - 0
=> -2b ( đpcm )

Answer 4

4. a ( b + c ) - a ( b + d )
=> a [ ( b + c ) - ( b + d )] 
=> a [ b + c - b - d ]
=> a [ ( b - b ) + ( c - d ) ]
=> a [ c - d ] ( đpcm )

Answer 5

5. a ( b - c ) + a ( d + c )
=> a [ b - c + d + c ]
=> a [ ( b + d ) - ( c - c ) ]
=> a [ b + d ] ( đpcm )