Math question???????/?

Question

Please don't just tell the answer. I actually want to know how to do this. And problems that are similar to this.
(a + 2b + 3c) - (4a + 6b - 5c) is equivalent to:

Answer 1

(a + 2b + 3c) - (4a + 6b - 5c)

Product of two different signs with negative.

a + 2b + 3c - 4a - 6b + 5c

(a - 4a) + (2b - 6b) + (3c + 5c)

(-3a) + (-4b)+ (8c).

Therefore -3a - 4b + 8c.

Comments

Could you please explain me what properties used for simplifying the problem?

Answer 2

(a + 2b + 3c) - (4a + 6b - 5c)

a + (2b + 3c) - 4a - 6b + 5c

 

Associative property of addition: a + b = b  + a

(2b + 3c) + a - 4a - 6b + 5c

 

Distributive property: ab - ac = a(b - c)

(2b + 3c) + a(1 - 4) - 6b + 5c

 

(2b + 3c) -3a - 6b + 5c

 

Similarly simplify other terms.

 

(-3a) + (-4b)+ (8c).