Simplify -(5ab+6a)+(ba-12a)-(7cb-2ab)+(bc+c)

$- (5 a b + 6 a) + (b a - 12 a) - (7 c b - 2 a b) + (b c + c)$

Step 1

Remove parentheses.

$- (5 a b + 6 a) + b a - 12 a - (7 c b - 2 a b) + b c + c$

Step 2

Simplify each term.

Apply the distributive property.

$- (5 a b) - (6 a) + b a - 12 a - (7 c b - 2 a b) + b c + c$

Multiply $5$ by $- 1$ .

$- 5 (a b) - (6 a) + b a - 12 a - (7 c b - 2 a b) + b c + c$

Multiply $6$ by $- 1$ .

$- 5 (a b) - 6 a + b a - 12 a - (7 c b - 2 a b) + b c + c$

Apply the distributive property.

$- 5 a b - 6 a + b a - 12 a - (7 c b) - (- 2 a b) + b c + c$

Multiply $7$ by $- 1$ .

$- 5 a b - 6 a + b a - 12 a - 7 (c b) - (- 2 a b) + b c + c$

Multiply $- 2$ by $- 1$ .

$- 5 a b - 6 a + b a - 12 a - 7 (c b) + 2 (a b) + b c + c$

Remove parentheses.

$- 5 a b - 6 a + b a - 12 a - 7 c b + 2 a b + b c + c$

Step 3

Add $- 5 a b$ and $b a$ .

Reorder $b$ and $a$ .

$- 6 a - 5 a b + a b - 12 a - 7 c b + 2 a b + b c + c$

Add $- 5 a b$ and $a b$ .

$- 6 a - 4 a b - 12 a - 7 c b + 2 a b + b c + c$

Step 4

Subtract $12 a$ from $- 6 a$ .

$- 18 a - 4 a b - 7 c b + 2 a b + b c + c$

Step 5

Add $- 4 a b$ and $2 a b$ .

$- 18 a - 2 a b - 7 c b + b c + c$

Step 6

Add $- 7 c b$ and $b c$ .

Move $c$ .

$- 18 a - 2 a b - 7 b c + b c + c$

Add $- 7 b c$ and $b c$ .

$- 18 a - 2 a b - 6 b c + c$

Step 7

Move $- 18 a$ .

$- 2 a b - 6 b c - 18 a + c$