Pre-Algebra Examples

$- 2 n (- 4 n - 2) + 2 n (6 - 6 n)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 n (- 4 n) - 2 n \cdot - 2 + 2 n (6 - 6 n)$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 4 n \cdot n - 2 n \cdot - 2 + 2 n (6 - 6 n)$

Step 1.3

Multiply $- 2$ by $- 2$ .

$- 2 \cdot - 4 n \cdot n + 4 n + 2 n (6 - 6 n)$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $n$ by $n$ by adding the exponents.

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Step 1.4.1.1

Move $n$ .

$- 2 \cdot - 4 (n \cdot n) + 4 n + 2 n (6 - 6 n)$

Step 1.4.1.2

Multiply $n$ by $n$ .

$- 2 \cdot - 4 n^{2} + 4 n + 2 n (6 - 6 n)$

Step 1.4.2

Multiply $- 2$ by $- 4$ .

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Multiply $6$ by $2$ .

$8 n^{2} + 4 n + 12 n + 2 n (- 6 n)$

Step 1.7

Rewrite using the commutative property of multiplication.

$8 n^{2} + 4 n + 12 n + 2 \cdot - 6 n \cdot n$

Step 1.8

Simplify each term.

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Step 1.8.1

Multiply $n$ by $n$ by adding the exponents.

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Step 1.8.1.1

Move $n$ .

$8 n^{2} + 4 n + 12 n + 2 \cdot - 6 (n \cdot n)$

Step 1.8.1.2

Multiply $n$ by $n$ .

$8 n^{2} + 4 n + 12 n + 2 \cdot - 6 n^{2}$

Step 1.8.2

Multiply $2$ by $- 6$ .

$8 n^{2} + 4 n + 12 n - 12 n^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 n^{2}$ from $8 n^{2}$ .

$- 4 n^{2} + 4 n + 12 n$

Step 2.2

Add $4 n$ and $12 n$ .

$- 4 n^{2} + 16 n$