Algebra Examples

$\frac{6 c^{2} d - 14 c d^{2} + 2 d^{3}}{2}$

Step 1

Factor $2 d$ out of $6 c^{2} d - 14 c d^{2} + 2 d^{3}$ .

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Step 1.1

Factor $2 d$ out of $6 c^{2} d$ .

$\frac{2 d (3 c^{2}) - 14 c d^{2} + 2 d^{3}}{2}$

Step 1.2

Factor $2 d$ out of $- 14 c d^{2}$ .

$\frac{2 d (3 c^{2}) + 2 d (- 7 c d) + 2 d^{3}}{2}$

Step 1.3

Factor $2 d$ out of $2 d^{3}$ .

$\frac{2 d (3 c^{2}) + 2 d (- 7 c d) + 2 d (d^{2})}{2}$

Step 1.4

Factor $2 d$ out of $2 d (3 c^{2}) + 2 d (- 7 c d)$ .

$\frac{2 d (3 c^{2} - 7 c d) + 2 d (d^{2})}{2}$

Step 1.5

Factor $2 d$ out of $2 d (3 c^{2} - 7 c d) + 2 d (d^{2})$ .

$\frac{2 d (3 c^{2} - 7 c d + d^{2})}{2}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{2 d (3 c^{2} - 7 c d + d^{2})}{2}$

Step 2.2

Divide $d (3 c^{2} - 7 c d + d^{2})$ by $1$ .

$d (3 c^{2} - 7 c d + d^{2})$

Step 3

Apply the distributive property.

$d (3 c^{2}) + d (- 7 c d) + d \cdot d^{2}$

Step 4

Simplify.

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Step 4.1

Rewrite using the commutative property of multiplication.

$3 d c^{2} + d (- 7 c d) + d \cdot d^{2}$

Step 4.2

Rewrite using the commutative property of multiplication.

$3 d c^{2} - 7 d (c d) + d \cdot d^{2}$

Step 4.3

Multiply $d$ by $d^{2}$ by adding the exponents.

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Step 4.3.1

Multiply $d$ by $d^{2}$ .

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Step 4.3.1.1

Raise $d$ to the power of $1$ .

$3 d c^{2} - 7 d (c d) + d^{1} d^{2}$

Step 4.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 d c^{2} - 7 d (c d) + d^{1 + 2}$

Step 4.3.2

Add $1$ and $2$ .

$3 d c^{2} - 7 d (c d) + d^{3}$

Step 5

Multiply $d$ by $d$ by adding the exponents.

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Step 5.1

Move $d$ .

$3 d c^{2} - 7 (d \cdot d) c + d^{3}$

Step 5.2

Multiply $d$ by $d$ .

$3 d c^{2} - 7 d^{2} c + d^{3}$

Step 6

Move $d$ .

$3 c^{2} d - 7 d^{2} c + d^{3}$

Step 7

Move $d^{2}$ .

$3 c^{2} d - 7 c d^{2} + d^{3}$