Basic Math Examples

$(2 c + 1) (2 c + 1) (2 c + 1)$

Step 1

Multiply $2 c + 1$ by $2 c + 1$ .

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

Step 2

Multiply ${(2 c + 1)}^{2}$ by $2 c + 1$ by adding the exponents.

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Step 2.1

Multiply ${(2 c + 1)}^{2}$ by $2 c + 1$ .

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Step 2.1.1

Raise $2 c + 1$ to the power of $1$ .

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

Step 2.1.2

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

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

Step 2.2

Add $2$ and $1$ .

${(2 c + 1)}^{3}$

Step 3

Use the Binomial Theorem.

${(2 c)}^{3} + 3 {(2 c)}^{2} \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4

Simplify each term.

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Step 4.1

Apply the product rule to $2 c$ .

$2^{3} c^{3} + 3 {(2 c)}^{2} \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.2

Raise $2$ to the power of $3$ .

$8 c^{3} + 3 {(2 c)}^{2} \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.3

Apply the product rule to $2 c$ .

$8 c^{3} + 3 (2^{2} c^{2}) \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.4

Raise $2$ to the power of $2$ .

$8 c^{3} + 3 (4 c^{2}) \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.5

Multiply $4$ by $3$ .

$8 c^{3} + 12 c^{2} \cdot 1 + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.6

Multiply $12$ by $1$ .

$8 c^{3} + 12 c^{2} + 3 (2 c) \cdot 1^{2} + 1^{3}$

Step 4.7

Multiply $2$ by $3$ .

$8 c^{3} + 12 c^{2} + 6 c \cdot 1^{2} + 1^{3}$

Step 4.8

One to any power is one.

$8 c^{3} + 12 c^{2} + 6 c \cdot 1 + 1^{3}$

Step 4.9

Multiply $6$ by $1$ .

$8 c^{3} + 12 c^{2} + 6 c + 1^{3}$

Step 4.10

One to any power is one.

$8 c^{3} + 12 c^{2} + 6 c + 1$