Basic Math Examples

$2 a^{2} (6 a^{2} + 4 a + 5)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Multiply $5$ by $2$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $a^{2}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Add $2$ and $2$ .

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

Step 3.2

Multiply $2$ by $6$ .

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

Step 3.3

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

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Step 3.3.1

Move $a$ .

$12 a^{4} + 2 \cdot 4 (a \cdot a^{2}) + 10 a^{2}$

Step 3.3.2

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

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Step 3.3.2.1

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

$12 a^{4} + 2 \cdot 4 (a^{1} a^{2}) + 10 a^{2}$

Step 3.3.2.2

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

$12 a^{4} + 2 \cdot 4 a^{1 + 2} + 10 a^{2}$

Step 3.3.3

Add $1$ and $2$ .

$12 a^{4} + 2 \cdot 4 a^{3} + 10 a^{2}$

Step 3.4

Multiply $2$ by $4$ .

$12 a^{4} + 8 a^{3} + 10 a^{2}$