Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $4$ by $3$ .

$- (a^{3} + 12 a^{2} + 3 a \cdot 4^{2} + 4^{3}) - 1$

Step 1.2.2

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

$- (a^{3} + 12 a^{2} + 3 a \cdot 16 + 4^{3}) - 1$

Step 1.2.3

Multiply $16$ by $3$ .

$- (a^{3} + 12 a^{2} + 48 a + 4^{3}) - 1$

Step 1.2.4

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

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

Step 1.3

Apply the distributive property.

$- a^{3} - (12 a^{2}) - (48 a) - 1 \cdot 64 - 1$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $12$ by $- 1$ .

$- a^{3} - 12 a^{2} - (48 a) - 1 \cdot 64 - 1$

Step 1.4.2

Multiply $48$ by $- 1$ .

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

Step 1.4.3

Multiply $- 1$ by $64$ .

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

Step 2

Subtract $1$ from $- 64$ .

$- a^{3} - 12 a^{2} - 48 a - 65$