Basic Math Examples

${(4 a + 1)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $4 a$ .

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

Step 2.2

Raise $4$ to the power of $3$ .

$64 a^{3} + 3 {(4 a)}^{2} \cdot 1 + 3 (4 a) \cdot 1^{2} + 1^{3}$

Step 2.3

Apply the product rule to $4 a$ .

$64 a^{3} + 3 (4^{2} a^{2}) \cdot 1 + 3 (4 a) \cdot 1^{2} + 1^{3}$

Step 2.4

Raise $4$ to the power of $2$ .

$64 a^{3} + 3 (16 a^{2}) \cdot 1 + 3 (4 a) \cdot 1^{2} + 1^{3}$

Step 2.5

Multiply $16$ by $3$ .

$64 a^{3} + 48 a^{2} \cdot 1 + 3 (4 a) \cdot 1^{2} + 1^{3}$

Step 2.6

Multiply $48$ by $1$ .

$64 a^{3} + 48 a^{2} + 3 (4 a) \cdot 1^{2} + 1^{3}$

Step 2.7

Multiply $4$ by $3$ .

$64 a^{3} + 48 a^{2} + 12 a \cdot 1^{2} + 1^{3}$

Step 2.8

One to any power is one.

$64 a^{3} + 48 a^{2} + 12 a \cdot 1 + 1^{3}$

Step 2.9

Multiply $12$ by $1$ .

$64 a^{3} + 48 a^{2} + 12 a + 1^{3}$

Step 2.10

One to any power is one.

$64 a^{3} + 48 a^{2} + 12 a + 1$