Algebra Examples

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

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.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $5$ by $- 1$ .

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

Step 2.3

Multiply $6$ by $- 1$ .

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

Step 2.4

Apply the distributive property.

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

Step 2.5

Multiply $7$ by $- 1$ .

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

Step 2.6

Multiply $- 2$ by $- 1$ .

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

Step 2.7

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 $b a$ .

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Step 3.1

Reorder $b$ and $a$ .

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

Step 3.2

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 $b c$ .

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Step 6.1

Move $c$ .

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

Step 6.2

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

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

Step 7

Move $- 18 a$ .

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