Basic Math Examples

$8 (3 a - 4 b + c) + 5 (2 a - 3 b + c) - 3 (2 c - 9 a + 7 b)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 (3 a) + 8 (- 4 b) + 8 c + 5 (2 a - 3 b + c) - 3 (2 c - 9 a + 7 b)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $8$ .

$24 a + 8 (- 4 b) + 8 c + 5 (2 a - 3 b + c) - 3 (2 c - 9 a + 7 b)$

Step 1.2.2

Multiply $- 4$ by $8$ .

$24 a - 32 b + 8 c + 5 (2 a - 3 b + c) - 3 (2 c - 9 a + 7 b)$

Step 1.3

Apply the distributive property.

$24 a - 32 b + 8 c + 5 (2 a) + 5 (- 3 b) + 5 c - 3 (2 c - 9 a + 7 b)$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $2$ by $5$ .

$24 a - 32 b + 8 c + 10 a + 5 (- 3 b) + 5 c - 3 (2 c - 9 a + 7 b)$

Step 1.4.2

Multiply $- 3$ by $5$ .

$24 a - 32 b + 8 c + 10 a - 15 b + 5 c - 3 (2 c - 9 a + 7 b)$

Step 1.5

Apply the distributive property.

$24 a - 32 b + 8 c + 10 a - 15 b + 5 c - 3 (2 c) - 3 (- 9 a) - 3 (7 b)$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $2$ by $- 3$ .

$24 a - 32 b + 8 c + 10 a - 15 b + 5 c - 6 c - 3 (- 9 a) - 3 (7 b)$

Step 1.6.2

Multiply $- 9$ by $- 3$ .

$24 a - 32 b + 8 c + 10 a - 15 b + 5 c - 6 c + 27 a - 3 (7 b)$

Step 1.6.3

Multiply $7$ by $- 3$ .

$24 a - 32 b + 8 c + 10 a - 15 b + 5 c - 6 c + 27 a - 21 b$

Step 2

Simplify by adding terms.

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Step 2.1

Add $24 a$ and $10 a$ .

$34 a - 32 b + 8 c - 15 b + 5 c - 6 c + 27 a - 21 b$

Step 2.2

Add $34 a$ and $27 a$ .

$61 a - 32 b + 8 c - 15 b + 5 c - 6 c - 21 b$

Step 2.3

Subtract $15 b$ from $- 32 b$ .

$61 a - 47 b + 8 c + 5 c - 6 c - 21 b$

Step 2.4

Subtract $21 b$ from $- 47 b$ .

$61 a - 68 b + 8 c + 5 c - 6 c$

Step 2.5

Add $8 c$ and $5 c$ .

$61 a - 68 b + 13 c - 6 c$

Step 2.6

Subtract $6 c$ from $13 c$ .

$61 a - 68 b + 7 c$