Simplify a-(4b-(a-(5b-c)+3c-(a-b-9c)))

$a - (4 b - (a - (5 b - c) + 3 c - (a - b - 9 c)))$

Step 1

Simplify each term.

Apply the distributive property.

$a - (4 b - (a - (5 b) - - c + 3 c - (a - b - 9 c)))$

Multiply $5$ by $- 1$ .

$a - (4 b - (a - 5 b - - c + 3 c - (a - b - 9 c)))$

Multiply $- - c$ .

Multiply $- 1$ by $- 1$ .

$a - (4 b - (a - 5 b + 1 c + 3 c - (a - b - 9 c)))$

Multiply $c$ by $1$ .

$a - (4 b - (a - 5 b + c + 3 c - (a - b - 9 c)))$

Apply the distributive property.

$a - (4 b - (a - 5 b + c + 3 c - a - - b - (- 9 c)))$

Simplify.

Multiply $- - b$ .

Multiply $- 1$ by $- 1$ .

$a - (4 b - (a - 5 b + c + 3 c - a + 1 b - (- 9 c)))$

Multiply $b$ by $1$ .

$a - (4 b - (a - 5 b + c + 3 c - a + b - (- 9 c)))$

Multiply $- 9$ by $- 1$ .

$a - (4 b - (a - 5 b + c + 3 c - a + b + 9 c))$

Combine the opposite terms in $a - 5 b + c + 3 c - a + b + 9 c$ .

Subtract $a$ from $a$ .

$a - (4 b - (- 5 b + c + 3 c + 0 + b + 9 c))$

Add $- 5 b + c + 3 c$ and $0$ .

$a - (4 b - (- 5 b + c + 3 c + b + 9 c))$

Add $- 5 b$ and $b$ .

$a - (4 b - (- 4 b + c + 3 c + 9 c))$

Add $c$ and $3 c$ .

$a - (4 b - (- 4 b + 4 c + 9 c))$

Add $4 c$ and $9 c$ .

$a - (4 b - (- 4 b + 13 c))$

Apply the distributive property.

$a - (4 b - (- 4 b) - (13 c))$

Multiply $- 4$ by $- 1$ .

$a - (4 b + 4 b - (13 c))$

Multiply $13$ by $- 1$ .

$a - (4 b + 4 b - 13 c)$

Step 2

Add $4 b$ and $4 b$ .

$a - (8 b - 13 c)$

Step 3

Apply the distributive property.

$a - (8 b) - (- 13 c)$

Step 4

Multiply $8$ by $- 1$ .

$a - 8 b - (- 13 c)$

Step 5

Multiply $- 13$ by $- 1$ .

$a - 8 b + 13 c$

Simplify a-(4b-(a-(5b-c)+3c-(a-b-9c)))

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