Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Rewrite using the commutative property of multiplication.

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

Step 1.2

Multiply $- 1$ by $2$ .

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

Step 1.3

Multiply $2$ by $- 2$ .

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $- 1$ by $2$ .

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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Step 5.1

Multiply $a$ by $a$ by adding the exponents.

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Step 5.1.1

Move $a$ .

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

Step 5.1.2

Multiply $a$ by $a$ .

$- 4 a^{2} b c \cdot 2 - 4 a b c (2 b) - 4 a b c (- 2 c)$

Step 5.2

Multiply $b$ by $b$ by adding the exponents.

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Step 5.2.1

Move $b$ .

$- 4 a^{2} b c \cdot 2 - 4 a (b \cdot b) c \cdot 2 - 4 a b c (- 2 c)$

Step 5.2.2

Multiply $b$ by $b$ .

$- 4 a^{2} b c \cdot 2 - 4 a b^{2} c \cdot 2 - 4 a b c (- 2 c)$

Step 5.3

Multiply $c$ by $c$ by adding the exponents.

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Step 5.3.1

Move $c$ .

$- 4 a^{2} b c \cdot 2 - 4 a b^{2} c \cdot 2 - 4 a b (c \cdot c) \cdot - 2$

Step 5.3.2

Multiply $c$ by $c$ .

$- 4 a^{2} b c \cdot 2 - 4 a b^{2} c \cdot 2 - 4 a b c^{2} \cdot - 2$

Step 6

Simplify each term.

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Step 6.1

Multiply $2$ by $- 4$ .

$- 8 a^{2} b c - 4 a b^{2} c \cdot 2 - 4 a b c^{2} \cdot - 2$

Step 6.2

Multiply $2$ by $- 4$ .

$- 8 a^{2} b c - 8 a b^{2} c - 4 a b c^{2} \cdot - 2$

Step 6.3

Multiply $- 2$ by $- 4$ .

$- 8 a^{2} b c - 8 a b^{2} c + 8 a b c^{2}$