Question

Bài 18: 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)

a(b – c) + a(d + c) = a(b + d)

Answer 1

a, Ta có : (a−b+c)−(a+c)=a−b+c−a−c=−b(a−b+c)−(a+c)=a−b+c−a−c=−b ( đpcm )

b, Ta có : (a+b)−(b−a)+c=a+b−b+a+c=2a+c(a+b)−(b−a)+c=a+b−b+a+c=2a+c (đpcm)

c, Ta có : −(a+b−c)+(a−b−c)=−a−b+c+a−b−c−(a+b−c)+(a−b−c)=−a−b+c+a−b−c

= −2b−2b ( đpcm )

d, Ta có : a(b+c)−a(b+d)=ab+ac−ab−ada(b+c)−a(b+d)=ab+ac−ab−ad

= ac−ad=a(c−d)ac−ad=a(c−d) ( đpcm )

e, Ta có : a(b−c)+a(d+c)=ab−ac+ad+aca(b−c)+a(d+c)=ab−ac+ad+ac

= ab+ad=a(b+d)ab+ad=a(b+d) ( đpcm )