Basic Math Examples

$2 n^{2} - 4 n \cdot (5 n) - 10 n^{2 + 4}$

Step 1

Factor $2$ out of $2 n^{2} - 4 n \cdot (5 n) - 10 n^{2 + 4}$ .

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Step 1.1

Factor $2$ out of $2 n^{2}$ .

$2 (n^{2}) - 4 n \cdot (5 n) - 10 n^{2 + 4}$

Step 1.2

Factor $2$ out of $- 4 n \cdot (5 n)$ .

$2 (n^{2}) + 2 (- 2 n \cdot (5 n)) - 10 n^{2 + 4}$

Step 1.3

Factor $2$ out of $- 10 n^{2 + 4}$ .

$2 (n^{2}) + 2 (- 2 n \cdot (5 n)) + 2 (- 5 n^{2 + 4})$

Step 1.4

Factor $2$ out of $2 (n^{2}) + 2 (- 2 n \cdot (5 n))$ .

$2 (n^{2} - 2 n \cdot (5 n)) + 2 (- 5 n^{2 + 4})$

Step 1.5

Factor $2$ out of $2 (n^{2} - 2 n \cdot (5 n)) + 2 (- 5 n^{2 + 4})$ .

$2 (n^{2} - 2 n \cdot (5 n) - 5 n^{2 + 4})$

Step 2

Rewrite using the commutative property of multiplication.

$2 (n^{2} - 2 \cdot 5 n \cdot n - 5 n^{2 + 4})$

Step 3

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

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Step 3.1

Move $n$ .

$2 (n^{2} - 2 \cdot 5 (n \cdot n) - 5 n^{2 + 4})$

Step 3.2

Multiply $n$ by $n$ .

$2 (n^{2} - 2 \cdot 5 n^{2} - 5 n^{2 + 4})$

Step 4

Multiply $- 2$ by $5$ .

$2 (n^{2} - 10 n^{2} - 5 n^{2 + 4})$

Step 5

Add $2$ and $4$ .

$2 (n^{2} - 10 n^{2} - 5 n^{6})$

Step 6

Subtract $10 n^{2}$ from $n^{2}$ .

$2 (- 9 n^{2} - 5 n^{6})$

Step 7

Factor.

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Step 7.1

Factor $n^{2}$ out of $- 9 n^{2} - 5 n^{6}$ .

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Step 7.1.1

Factor $n^{2}$ out of $- 9 n^{2}$ .

$2 (n^{2} \cdot - 9 - 5 n^{6})$

Step 7.1.2

Factor $n^{2}$ out of $- 5 n^{6}$ .

$2 (n^{2} \cdot - 9 + n^{2} (- 5 n^{4}))$

Step 7.1.3

Factor $n^{2}$ out of $n^{2} \cdot - 9 + n^{2} (- 5 n^{4})$ .

$2 (n^{2} (- 9 - 5 n^{4}))$

Step 7.2

Remove unnecessary parentheses.

$2 n^{2} (- 9 - 5 n^{4})$

Step 8

Factor.

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Step 8.1

Factor $- 1$ out of $- 9 - 5 n^{4}$ .

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Step 8.1.1

Reorder $- 9$ and $- 5 n^{4}$ .

$2 n^{2} (- 5 n^{4} - 9)$

Step 8.1.2

Factor $- 1$ out of $- 5 n^{4}$ .

$2 n^{2} (- (5 n^{4}) - 9)$

Step 8.1.3

Rewrite $- 9$ as $- 1 (9)$ .

$2 n^{2} (- (5 n^{4}) - 1 (9))$

Step 8.1.4

Factor $- 1$ out of $- (5 n^{4}) - 1 (9)$ .

$2 n^{2} (- (5 n^{4} + 9))$

Step 8.2

Remove unnecessary parentheses.

$2 n^{2} \cdot - 1 (5 n^{4} + 9)$

Step 9

Combine exponents.

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Step 9.1

Factor out negative.

$- (2 n^{2} (5 n^{4} + 9))$

Step 9.2

Multiply $2$ by $- 1$ .

$- 2 (n^{2} (5 n^{4} + 9))$

Step 10

Remove unnecessary parentheses.

$- 2 n^{2} (5 n^{4} + 9)$