Basic Math Examples

$a (- 8 a^{2} + 2 a + 4) + 3 (6 a^{2} - 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a (- 8 a^{2}) + a (2 a) + a \cdot 4 + 3 (6 a^{2} - 4)$

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$- 8 a \cdot a^{2} + a (2 a) + a \cdot 4 + 3 (6 a^{2} - 4)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- 8 a \cdot a^{2} + 2 a \cdot a + a \cdot 4 + 3 (6 a^{2} - 4)$

Step 1.2.3

Move $4$ to the left of $a$ .

$- 8 a \cdot a^{2} + 2 a \cdot a + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $a^{2}$ .

$- 8 (a^{2} a) + 2 a \cdot a + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

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

$- 8 (a^{2} a^{1}) + 2 a \cdot a + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3.1.2.2

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

$- 8 a^{2 + 1} + 2 a \cdot a + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3.1.3

Add $2$ and $1$ .

$- 8 a^{3} + 2 a \cdot a + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3.2

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

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Step 1.3.2.1

Move $a$ .

$- 8 a^{3} + 2 (a \cdot a) + 4 \cdot a + 3 (6 a^{2} - 4)$

Step 1.3.2.2

Multiply $a$ by $a$ .

$- 8 a^{3} + 2 a^{2} + 4 \cdot a + 3 (6 a^{2} - 4)$

$- 8 a^{3} + 2 a^{2} + 4 a + 3 (6 a^{2} - 4)$

Step 1.4

Apply the distributive property.

$- 8 a^{3} + 2 a^{2} + 4 a + 3 (6 a^{2}) + 3 \cdot - 4$

Step 1.5

Multiply $6$ by $3$ .

$- 8 a^{3} + 2 a^{2} + 4 a + 18 a^{2} + 3 \cdot - 4$

Step 1.6

Multiply $3$ by $- 4$ .

$- 8 a^{3} + 2 a^{2} + 4 a + 18 a^{2} - 12$

Step 2

Add $2 a^{2}$ and $18 a^{2}$ .

$- 8 a^{3} + 20 a^{2} + 4 a - 12$