Basic Math Examples

$8 a (a + 3) - 2 a (12 + 4 a)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 a \cdot a + 8 a \cdot 3 - 2 a (12 + 4 a)$

Step 1.2

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

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Step 1.2.1

Move $a$ .

$8 (a \cdot a) + 8 a \cdot 3 - 2 a (12 + 4 a)$

Step 1.2.2

Multiply $a$ by $a$ .

$8 a^{2} + 8 a \cdot 3 - 2 a (12 + 4 a)$

Step 1.3

Multiply $3$ by $8$ .

$8 a^{2} + 24 a - 2 a (12 + 4 a)$

Step 1.4

Apply the distributive property.

$8 a^{2} + 24 a - 2 a \cdot 12 - 2 a (4 a)$

Step 1.5

Multiply $12$ by $- 2$ .

$8 a^{2} + 24 a - 24 a - 2 a (4 a)$

Step 1.6

Rewrite using the commutative property of multiplication.

$8 a^{2} + 24 a - 24 a - 2 \cdot 4 a \cdot a$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $a$ .

$8 a^{2} + 24 a - 24 a - 2 \cdot 4 (a \cdot a)$

Step 1.7.1.2

Multiply $a$ by $a$ .

$8 a^{2} + 24 a - 24 a - 2 \cdot 4 a^{2}$

Step 1.7.2

Multiply $- 2$ by $4$ .

$8 a^{2} + 24 a - 24 a - 8 a^{2}$

Step 2

Combine the opposite terms in $8 a^{2} + 24 a - 24 a - 8 a^{2}$ .

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Step 2.1

Subtract $24 a$ from $24 a$ .

$8 a^{2} + 0 - 8 a^{2}$

Step 2.2

Add $8 a^{2}$ and $0$ .

$8 a^{2} - 8 a^{2}$

Step 2.3

Subtract $8 a^{2}$ from $8 a^{2}$ .

$0$