Basic Math Examples

$(9 n^{3} - 7 n - 5 + 4 n^{2}) - (5 n^{3} + 4 n^{2} + 7 n - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 n^{3} - 7 n - 5 + 4 n^{2} - (5 n^{3}) - (4 n^{2}) - (7 n) - - 5$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$9 n^{3} - 7 n - 5 + 4 n^{2} - 5 n^{3} - (4 n^{2}) - (7 n) - - 5$

Step 1.2.2

Multiply $4$ by $- 1$ .

$9 n^{3} - 7 n - 5 + 4 n^{2} - 5 n^{3} - 4 n^{2} - (7 n) - - 5$

Step 1.2.3

Multiply $7$ by $- 1$ .

$9 n^{3} - 7 n - 5 + 4 n^{2} - 5 n^{3} - 4 n^{2} - 7 n - - 5$

Step 1.2.4

Multiply $- 1$ by $- 5$ .

$9 n^{3} - 7 n - 5 + 4 n^{2} - 5 n^{3} - 4 n^{2} - 7 n + 5$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $9 n^{3} - 7 n - 5 + 4 n^{2} - 5 n^{3} - 4 n^{2} - 7 n + 5$ .

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Step 2.1.1

Subtract $4 n^{2}$ from $4 n^{2}$ .

$9 n^{3} - 7 n - 5 - 5 n^{3} + 0 - 7 n + 5$

Step 2.1.2

Add $9 n^{3} - 7 n - 5 - 5 n^{3}$ and $0$ .

$9 n^{3} - 7 n - 5 - 5 n^{3} - 7 n + 5$

Step 2.1.3

Add $- 5$ and $5$ .

$9 n^{3} - 7 n - 5 n^{3} - 7 n + 0$

Step 2.1.4

Add $9 n^{3} - 7 n - 5 n^{3} - 7 n$ and $0$ .

$9 n^{3} - 7 n - 5 n^{3} - 7 n$

Step 2.2

Subtract $5 n^{3}$ from $9 n^{3}$ .

$4 n^{3} - 7 n - 7 n$

Step 2.3

Subtract $7 n$ from $- 7 n$ .

$4 n^{3} - 14 n$