Basic Math Examples

$z^{3} - z^{2} + 7 z (2 z + 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

$z^{3} - z^{2} + 7 \cdot 2 z \cdot z + 7 z \cdot 3$

Step 1.3

Multiply $3$ by $7$ .

$z^{3} - z^{2} + 7 \cdot 2 z \cdot z + 21 z$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $z$ .

$z^{3} - z^{2} + 7 \cdot 2 (z \cdot z) + 21 z$

Step 1.4.1.2

Multiply $z$ by $z$ .

$z^{3} - z^{2} + 7 \cdot 2 z^{2} + 21 z$

Step 1.4.2

Multiply $7$ by $2$ .

$z^{3} - z^{2} + 14 z^{2} + 21 z$

Step 2

Add $- z^{2}$ and $14 z^{2}$ .

$z^{3} + 13 z^{2} + 21 z$