Question

Thu gọn các biểu thức:

a) (a + b - c) + (b + c - a) + (a +​c - b); b) (a - b) + (b - c + a) + (c - b).

c) (2a - b + c) + (b - c + a) + (c - 2a + b); d) (a - c + b) + (b - c - a) - a - b - c;

Answer 1

\( a)\left( {a + b - c} \right) + \left( {b + c - a} \right) + \left( {a + c - b} \right)\\ = a + b - c + b + c - a + a + c - b\\ = a + b + c\\ b)\left( {a - b} \right) + \left( {b - c + a} \right) + \left( {c - b} \right)\\ = a - b + b - c + a + c - b\\ = 2a + b\\ c)\left( {2a - b + c} \right) + \left( {b - c + a} \right) + \left( {c - 2a + b} \right)\\ = 2a - b + c + b - c + a + c - 2a + b\\ = a + b + c\\ d)\left( {a - c + b} \right) + \left( {b - c - a} \right) - a - b - c\\ = a - c + b + b - c - a - a - b - c\\ = - a - b - 3c \)

Answer 2

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

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

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

= a + b + c

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

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

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

= 2a - b

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

= 2a - b + c + b - c + a + c - 2a + b

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

= b + c

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

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

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

= b - 2a - 3c

Chúc bạn học tốt@@

Answer 3

a/ \((a + b - c) + (b + c - a) + (a +​c - b)\)

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

\(=\left(a-a\right)+\left(b-b\right)+\left(-c+c\right)+a+b+c\)

\(=a+b+c\)

b/ \(\text{ (a - b) + (b - c + a) + (c - b)}\)

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

\(=\left(a+a\right)+\left(-b+b\right)-\left(c-c\right)-b\)

\(=2a-b\)

c/ \(\text{(2a - b + c) + (b - c + a) + (c - 2a + b)}\)

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

\(=\left(2a-2a\right)-\left(b-b\right)+\left(c-c\right)+a+b+c\)

\(=a+b+c\)

d) \(\text{(a - c + b) + (b - c - a) - a - b - c}\)

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

\(=\left(a-a\right)+\left(b-b\right)-\left(c+c+c\right)-a+b\)

\(=-\left(3c\right)-a+b\)