Algebra Examples

$- \frac{1}{2} c (4 c - 2)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$- \frac{1}{2} \cdot (c (4 c) + c \cdot - 2)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$- \frac{1}{2} \cdot (4 c \cdot c + c \cdot - 2)$

Step 1.2.2

Move $- 2$ to the left of $c$ .

$- \frac{1}{2} \cdot (4 c \cdot c - 2 \cdot c)$

Step 2

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

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Step 2.1

Move $c$ .

$- \frac{1}{2} \cdot (4 (c \cdot c) - 2 \cdot c)$

Step 2.2

Multiply $c$ by $c$ .

$- \frac{1}{2} \cdot (4 c^{2} - 2 \cdot c)$

$- \frac{1}{2} \cdot (4 c^{2} - 2 c)$

Step 3

Simplify terms.

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Step 3.1

Apply the distributive property.

$- \frac{1}{2} (4 c^{2}) - \frac{1}{2} (- 2 c)$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (4 c^{2}) - \frac{1}{2} (- 2 c)$

Step 3.2.2

Factor $2$ out of $4 c^{2}$ .

$\frac{- 1}{2} (2 (2 c^{2})) - \frac{1}{2} (- 2 c)$

Step 3.2.3

Cancel the common factor.

$\frac{- 1}{2} (2 (2 c^{2})) - \frac{1}{2} (- 2 c)$

Step 3.2.4

Rewrite the expression.

$- 1 (2 c^{2}) - \frac{1}{2} (- 2 c)$

Step 3.3

Multiply $2$ by $- 1$ .

$- 2 c^{2} - \frac{1}{2} (- 2 c)$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 c^{2} + \frac{- 1}{2} (- 2 c)$

Step 3.4.2

Factor $2$ out of $- 2 c$ .

$- 2 c^{2} + \frac{- 1}{2} (2 (- c))$

Step 3.4.3

Cancel the common factor.

$- 2 c^{2} + \frac{- 1}{2} (2 (- c))$

Step 3.4.4

Rewrite the expression.

$- 2 c^{2} - 1 (- c)$

Step 3.5

Multiply.

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Step 3.5.1

Multiply $- 1$ by $- 1$ .

$- 2 c^{2} + 1 c$

Step 3.5.2

Multiply $c$ by $1$ .

$- 2 c^{2} + c$