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)
5/ a(b – c) + a(d + c) = a(b + d)

Answer 1

1/ (a + b + c) – (a + c) = b

(a + b + c) - (a + c)

= a + b + c - a - c

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

= 0 + b

= b

Vậy: (a + b + c) - (a + c) = b (đpcm)

2/ (a + b) – (b – a) - c = 2a - c

(a + b) - (b - a) - c

= a + b - b + a - c

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

= 2a + 0 - c

= 2a - c

Vậy: (a + b) – (b – a) - c = 2a - c (đpcm)

3/ - (a + b – c) + (a – b – c) = -2b

- (a + b - c) + (a - b - c)

= -a - b + c + a - b - c

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

= 0 + (-2b) + 0

= -2b

Vậy: - (a + b – c) + (a – b – c) = -2b (đpcm)

4/ a(b + c) – a(b + d) = a(c – d)

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

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

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

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

= a. (0 + c - d)

= a. (c - d)

Vậy: a. (b + c) – a. (b + d) = a. (c – d)

5/ a. (b – c) + a. (d + c) = a. (b + d)

a. (b – c) + a. (d + c)

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

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

= a. (b + d)

Vậy: a. (b – c) + a. (d + c) = a. (b + d)