Basic Math Examples

2 \cdot (2 a - b \cdot (2 a - c \cdot (2 a - 1) + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - c \cdot (2 a - 1) + 2 a c) - c)$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

2 \cdot (2 a - b \cdot (2 a - c (2 a) - c \cdot - 1 + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - c (2 a) - c \cdot - 1 + 2 a c) - c)$

Step 1.1.2

Rewrite using the commutative property of multiplication.

2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a - c \cdot - 1 + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a - c \cdot - 1 + 2 a c) - c)$

Step 1.1.3

Multiply

- c \cdot - 1

$- c \cdot - 1$ .

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Step 1.1.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + 1 c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + 1 c + 2 a c) - c)$

Step 1.1.3.2

Multiply

c

$c$ by

1

$1$ .

2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + c + 2 a c) - c)$

2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 1 \cdot 2 c a + c + 2 a c) - c)$

Step 1.1.4

Multiply

- 1

$- 1$ by

2

$2$ .

2 \cdot (2 a - b \cdot (2 a - 2 c a + c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 2 c a + c + 2 a c) - c)$

2 \cdot (2 a - b \cdot (2 a - 2 c a + c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 2 c a + c + 2 a c) - c)$

Step 1.2

Combine the opposite terms in

2 a - 2 c a + c + 2 a c

$2 a - 2 c a + c + 2 a c$ .

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Step 1.2.1

Reorder the factors in the terms

- 2 c a

$- 2 c a$ and

2 a c

$2 a c$ .

2 \cdot (2 a - b \cdot (2 a - 2 a c + c + 2 a c) - c)

$2 \cdot (2 a - b \cdot (2 a - 2 a c + c + 2 a c) - c)$

Step 1.2.2

Add

- 2 a c

$- 2 a c$ and

2 a c

$2 a c$ .

2 \cdot (2 a - b \cdot (2 a + c + 0) - c)

$2 \cdot (2 a - b \cdot (2 a + c + 0) - c)$

Step 1.2.3

Add

2 a + c

$2 a + c$ and

0

$0$ .

2 \cdot (2 a - b \cdot (2 a + c) - c)

$2 \cdot (2 a - b \cdot (2 a + c) - c)$

2 \cdot (2 a - b \cdot (2 a + c) - c)

$2 \cdot (2 a - b \cdot (2 a + c) - c)$

Step 1.3

Apply the distributive property.

2 \cdot (2 a - b (2 a) - b c - c)

$2 \cdot (2 a - b (2 a) - b c - c)$

Step 1.4

Rewrite using the commutative property of multiplication.

2 \cdot (2 a - 1 \cdot 2 b a - b c - c)

$2 \cdot (2 a - 1 \cdot 2 b a - b c - c)$

Step 1.5

Multiply

- 1

$- 1$ by

2

$2$ .

2 \cdot (2 a - 2 b a - b c - c)

$2 \cdot (2 a - 2 b a - b c - c)$

2 \cdot (2 a - 2 b a - b c - c)

$2 \cdot (2 a - 2 b a - b c - c)$

Step 2

Apply the distributive property.

2 (2 a) + 2 (- 2 b a) + 2 (- b c) + 2 (- c)

$2 (2 a) + 2 (- 2 b a) + 2 (- b c) + 2 (- c)$

Step 3

Simplify.

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Step 3.1

Multiply

2

$2$ by

2

$2$ .

4 a + 2 (- 2 b a) + 2 (- b c) + 2 (- c)

$4 a + 2 (- 2 b a) + 2 (- b c) + 2 (- c)$

Step 3.2

Multiply

- 2

$- 2$ by

2

$2$ .

4 a - 4 (b a) + 2 (- b c) + 2 (- c)

$4 a - 4 (b a) + 2 (- b c) + 2 (- c)$

Step 3.3

Multiply

- 1

$- 1$ by

2

$2$ .

4 a - 4 (b a) - 2 (b c) + 2 (- c)

$4 a - 4 (b a) - 2 (b c) + 2 (- c)$

Step 3.4

Multiply

- 1

$- 1$ by

2

$2$ .

4 a - 4 (b a) - 2 (b c) - 2 c

$4 a - 4 (b a) - 2 (b c) - 2 c$

4 a - 4 (b a) - 2 (b c) - 2 c

$4 a - 4 (b a) - 2 (b c) - 2 c$

Step 4

Remove parentheses.

4 a - 4 b a - 2 b c - 2 c

$4 a - 4 b a - 2 b c - 2 c$

Step 5

Reorder.

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Step 5.1

Move

b

$b$ .

4 a - 4 a b - 2 b c - 2 c

$4 a - 4 a b - 2 b c - 2 c$

Step 5.2

Move

4 a

$4 a$ .

- 4 a b - 2 b c + 4 a - 2 c

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

- 4 a b - 2 b c + 4 a - 2 c

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