Basic Math Examples

$(3 z - 2) (z + 5) + 4 (z + 5)$

Step 1

Simplify each term.

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Step 1.1

Expand $(3 z - 2) (z + 5)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$3 z (z + 5) - 2 (z + 5) + 4 (z + 5)$

Step 1.1.2

Apply the distributive property.

$3 z \cdot z + 3 z \cdot 5 - 2 (z + 5) + 4 (z + 5)$

Step 1.1.3

Apply the distributive property.

$3 z \cdot z + 3 z \cdot 5 - 2 z - 2 \cdot 5 + 4 (z + 5)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Move $z$ .

$3 (z \cdot z) + 3 z \cdot 5 - 2 z - 2 \cdot 5 + 4 (z + 5)$

Step 1.2.1.1.2

Multiply $z$ by $z$ .

$3 z^{2} + 3 z \cdot 5 - 2 z - 2 \cdot 5 + 4 (z + 5)$

Step 1.2.1.2

Multiply $5$ by $3$ .

$3 z^{2} + 15 z - 2 z - 2 \cdot 5 + 4 (z + 5)$

Step 1.2.1.3

Multiply $- 2$ by $5$ .

$3 z^{2} + 15 z - 2 z - 10 + 4 (z + 5)$

Step 1.2.2

Subtract $2 z$ from $15 z$ .

$3 z^{2} + 13 z - 10 + 4 (z + 5)$

Step 1.3

Apply the distributive property.

$3 z^{2} + 13 z - 10 + 4 z + 4 \cdot 5$

Step 1.4

Multiply $4$ by $5$ .

$3 z^{2} + 13 z - 10 + 4 z + 20$

Step 2

Simplify by adding terms.

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Step 2.1

Add $13 z$ and $4 z$ .

$3 z^{2} + 17 z - 10 + 20$

Step 2.2

Add $- 10$ and $20$ .

$3 z^{2} + 17 z + 10$