Basic Math Examples

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

Step 1

Expand $(2 a - 4) (3 a + 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.2.1

Move $a$ .

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

Step 2.1.2.2

Multiply $a$ by $a$ .

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

Step 2.1.3

Multiply $2$ by $3$ .

$6 a^{2} + 2 a \cdot 5 - 4 (3 a) - 4 \cdot 5$

Step 2.1.4

Multiply $5$ by $2$ .

$6 a^{2} + 10 a - 4 (3 a) - 4 \cdot 5$

Step 2.1.5

Multiply $3$ by $- 4$ .

$6 a^{2} + 10 a - 12 a - 4 \cdot 5$

Step 2.1.6

Multiply $- 4$ by $5$ .

$6 a^{2} + 10 a - 12 a - 20$

Step 2.2

Subtract $12 a$ from $10 a$ .

$6 a^{2} - 2 a - 20$