Basic Math Examples

$z^{3} - (z^{2} - 3 z) (z + 3)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$z^{3} + (- z^{2} - (- 3 z)) (z + 3)$

Step 1.2

Multiply $- 3$ by $- 1$ .

$z^{3} + (- z^{2} + 3 z) (z + 3)$

Step 1.3

Expand $(- z^{2} + 3 z) (z + 3)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$z^{3} - z^{2} (z + 3) + 3 z (z + 3)$

Step 1.3.2

Apply the distributive property.

$z^{3} - z^{2} z - z^{2} \cdot 3 + 3 z (z + 3)$

Step 1.3.3

Apply the distributive property.

$z^{3} - z^{2} z - z^{2} \cdot 3 + 3 z \cdot z + 3 z \cdot 3$

Step 1.4

Simplify and combine like terms.

Tap for more steps...

Step 1.4.1

Simplify each term.

Tap for more steps...

Step 1.4.1.1

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

Tap for more steps...

Step 1.4.1.1.1

Move $z$ .

$z^{3} - (z \cdot z^{2}) - z^{2} \cdot 3 + 3 z \cdot z + 3 z \cdot 3$

Step 1.4.1.1.2

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

Tap for more steps...

Step 1.4.1.1.2.1

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

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

Step 1.4.1.1.2.2

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

$z^{3} - z^{1 + 2} - z^{2} \cdot 3 + 3 z \cdot z + 3 z \cdot 3$

Step 1.4.1.1.3

Add $1$ and $2$ .

$z^{3} - z^{3} - z^{2} \cdot 3 + 3 z \cdot z + 3 z \cdot 3$

Step 1.4.1.2

Multiply $3$ by $- 1$ .

$z^{3} - z^{3} - 3 z^{2} + 3 z \cdot z + 3 z \cdot 3$

Step 1.4.1.3

Multiply $z$ by $z$ by adding the exponents.

Tap for more steps...

Step 1.4.1.3.1

Move $z$ .

$z^{3} - z^{3} - 3 z^{2} + 3 (z \cdot z) + 3 z \cdot 3$

Step 1.4.1.3.2

Multiply $z$ by $z$ .

$z^{3} - z^{3} - 3 z^{2} + 3 z^{2} + 3 z \cdot 3$

Step 1.4.1.4

Multiply $3$ by $3$ .

$z^{3} - z^{3} - 3 z^{2} + 3 z^{2} + 9 z$

Step 1.4.2

Add $- 3 z^{2}$ and $3 z^{2}$ .

$z^{3} - z^{3} + 0 + 9 z$

Step 1.4.3

Add $- z^{3}$ and $0$ .

$z^{3} - z^{3} + 9 z$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $z^{3}$ from $z^{3}$ .

$0 + 9 z$

Step 2.2

Add $0$ and $9 z$ .

$9 z$