Basic Math Examples

$- 2 a (- 7 a^{3} + 6) + (- 2 a) (6 a^{3} - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 a (- 7 a^{3}) - 2 a \cdot 6 + (- 2 a) (6 a^{3} - 5)$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 7 a \cdot a^{3} - 2 a \cdot 6 + (- 2 a) (6 a^{3} - 5)$

Step 1.3

Multiply $6$ by $- 2$ .

$- 2 \cdot - 7 a \cdot a^{3} - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $a^{3}$ .

$- 2 \cdot - 7 (a^{3} a) - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$- 2 \cdot - 7 (a^{3} a^{1}) - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.4.1.2.2

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

$- 2 \cdot - 7 a^{3 + 1} - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.4.1.3

Add $3$ and $1$ .

$- 2 \cdot - 7 a^{4} - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.4.2

Multiply $- 2$ by $- 7$ .

$14 a^{4} - 12 a + (- 2 a) (6 a^{3} - 5)$

Step 1.5

Apply the distributive property.

$14 a^{4} - 12 a - 2 a (6 a^{3}) - 2 a \cdot - 5$

Step 1.6

Rewrite using the commutative property of multiplication.

$14 a^{4} - 12 a - 2 \cdot 6 a \cdot a^{3} - 2 a \cdot - 5$

Step 1.7

Multiply $- 5$ by $- 2$ .

$14 a^{4} - 12 a - 2 \cdot 6 a \cdot a^{3} + 10 a$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $a^{3}$ .

$14 a^{4} - 12 a - 2 \cdot 6 (a^{3} a) + 10 a$

Step 1.8.1.2

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

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Step 1.8.1.2.1

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

$14 a^{4} - 12 a - 2 \cdot 6 (a^{3} a^{1}) + 10 a$

Step 1.8.1.2.2

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

$14 a^{4} - 12 a - 2 \cdot 6 a^{3 + 1} + 10 a$

Step 1.8.1.3

Add $3$ and $1$ .

$14 a^{4} - 12 a - 2 \cdot 6 a^{4} + 10 a$

Step 1.8.2

Multiply $- 2$ by $6$ .

$14 a^{4} - 12 a - 12 a^{4} + 10 a$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 a^{4}$ from $14 a^{4}$ .

$2 a^{4} - 12 a + 10 a$

Step 2.2

Add $- 12 a$ and $10 a$ .

$2 a^{4} - 2 a$