Trigonometry Examples

$100 a + 8 c - 6 a + (20 a - 12 c) - (16 a - 9 c) - (23 a - 11 c + 7) - 9 c$

Step 1

Remove parentheses.

$100 a + 8 c - 6 a + 20 a - 12 c - (16 a - 9 c) - (23 a - 11 c + 7) - 9 c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$100 a + 8 c - 6 a + 20 a - 12 c - (16 a) - (- 9 c) - (23 a - 11 c + 7) - 9 c$

Step 2.2

Multiply $16$ by $- 1$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a - (- 9 c) - (23 a - 11 c + 7) - 9 c$

Step 2.3

Multiply $- 9$ by $- 1$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - (23 a - 11 c + 7) - 9 c$

Step 2.4

Apply the distributive property.

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - (23 a) - (- 11 c) - 1 \cdot 7 - 9 c$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $23$ by $- 1$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - 23 a - (- 11 c) - 1 \cdot 7 - 9 c$

Step 2.5.2

Multiply $- 11$ by $- 1$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - 23 a + 11 c - 1 \cdot 7 - 9 c$

Step 2.5.3

Multiply $- 1$ by $7$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - 23 a + 11 c - 7 - 9 c$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $100 a + 8 c - 6 a + 20 a - 12 c - 16 a + 9 c - 23 a + 11 c - 7 - 9 c$ .

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Step 3.1.1

Subtract $9 c$ from $9 c$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a - 23 a + 11 c - 7 + 0$

Step 3.1.2

Add $100 a + 8 c - 6 a + 20 a - 12 c - 16 a - 23 a + 11 c - 7$ and $0$ .

$100 a + 8 c - 6 a + 20 a - 12 c - 16 a - 23 a + 11 c - 7$

Step 3.2

Subtract $6 a$ from $100 a$ .

$94 a + 8 c + 20 a - 12 c - 16 a - 23 a + 11 c - 7$

Step 3.3

Add $94 a$ and $20 a$ .

$114 a + 8 c - 12 c - 16 a - 23 a + 11 c - 7$

Step 3.4

Subtract $16 a$ from $114 a$ .

$98 a + 8 c - 12 c - 23 a + 11 c - 7$

Step 3.5

Subtract $23 a$ from $98 a$ .

$75 a + 8 c - 12 c + 11 c - 7$

Step 3.6

Subtract $12 c$ from $8 c$ .

$75 a - 4 c + 11 c - 7$

Step 3.7

Add $- 4 c$ and $11 c$ .

$75 a + 7 c - 7$