Algebra Examples

$2 a (a^{2} - 7) (a + 2)$

Step 1

Apply the distributive property.

$(2 a \cdot a^{2} + 2 a \cdot - 7) (a + 2)$

Step 2

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

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Step 2.1

Move $a^{2}$ .

$(2 (a^{2} a) + 2 a \cdot - 7) (a + 2)$

Step 2.2

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

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Step 2.2.1

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

$(2 (a^{2} a^{1}) + 2 a \cdot - 7) (a + 2)$

Step 2.2.2

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

$(2 a^{2 + 1} + 2 a \cdot - 7) (a + 2)$

Step 2.3

Add $2$ and $1$ .

$(2 a^{3} + 2 a \cdot - 7) (a + 2)$

Step 3

Multiply $- 7$ by $2$ .

$(2 a^{3} - 14 a) (a + 2)$

Step 4

Expand $(2 a^{3} - 14 a) (a + 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$2 a^{3} (a + 2) - 14 a (a + 2)$

Step 4.2

Apply the distributive property.

$2 a^{3} a + 2 a^{3} \cdot 2 - 14 a (a + 2)$

Step 4.3

Apply the distributive property.

$2 a^{3} a + 2 a^{3} \cdot 2 - 14 a \cdot a - 14 a \cdot 2$

Step 5

Simplify each term.

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Step 5.1

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 5.1.1

Move $a$ .

$2 (a \cdot a^{3}) + 2 a^{3} \cdot 2 - 14 a \cdot a - 14 a \cdot 2$

Step 5.1.2

Multiply $a$ by $a^{3}$ .

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Step 5.1.2.1

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

$2 (a^{1} a^{3}) + 2 a^{3} \cdot 2 - 14 a \cdot a - 14 a \cdot 2$

Step 5.1.2.2

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

$2 a^{1 + 3} + 2 a^{3} \cdot 2 - 14 a \cdot a - 14 a \cdot 2$

Step 5.1.3

Add $1$ and $3$ .

$2 a^{4} + 2 a^{3} \cdot 2 - 14 a \cdot a - 14 a \cdot 2$

Step 5.2

Multiply $2$ by $2$ .

$2 a^{4} + 4 a^{3} - 14 a \cdot a - 14 a \cdot 2$

Step 5.3

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

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Step 5.3.1

Move $a$ .

$2 a^{4} + 4 a^{3} - 14 (a \cdot a) - 14 a \cdot 2$

Step 5.3.2

Multiply $a$ by $a$ .

$2 a^{4} + 4 a^{3} - 14 a^{2} - 14 a \cdot 2$

Step 5.4

Multiply $2$ by $- 14$ .

$2 a^{4} + 4 a^{3} - 14 a^{2} - 28 a$