Basic Math Examples

$(2 n + 1) \cdot (2 n) - n (n - 1) (n - 2)$

Step 1

Remove parentheses.

$(2 n + 1) \cdot 2 n - n (n - 1) (n - 2)$

Step 2

Factor $n$ out of $(2 n + 1) \cdot 2 n - n (n - 1) (n - 2)$ .

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Step 2.1

Factor $n$ out of $(2 n + 1) \cdot 2 n$ .

$n ((2 n + 1) \cdot 2) - n (n - 1) (n - 2)$

Step 2.2

Factor $n$ out of $- n (n - 1) (n - 2)$ .

$n ((2 n + 1) \cdot 2) + n ((- 1 (n - 1)) (n - 2))$

Step 2.3

Factor $n$ out of $n ((2 n + 1) \cdot 2) + n ((- 1 (n - 1)) (n - 2))$ .

$n ((2 n + 1) \cdot 2 + (- 1 (n - 1)) (n - 2))$

Step 3

Apply the distributive property.

$n (2 n \cdot 2 + 1 \cdot 2 + (- 1 (n - 1)) (n - 2))$

Step 4

Multiply $2$ by $2$ .

$n (4 n + 1 \cdot 2 + (- 1 (n - 1)) (n - 2))$

Step 5

Multiply $2$ by $1$ .

$n (4 n + 2 + (- 1 (n - 1)) (n - 2))$

Step 6

Apply the distributive property.

$n (4 n + 2 + (- 1 n - 1 \cdot - 1) (n - 2))$

Step 7

Rewrite $- 1 n$ as $- n$ .

$n (4 n + 2 + (- n - 1 \cdot - 1) (n - 2))$

Step 8

Multiply $- 1$ by $- 1$ .

$n (4 n + 2 + (- n + 1) (n - 2))$

Step 9

Expand $(- n + 1) (n - 2)$ using the FOIL Method.

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Step 9.1

Apply the distributive property.

$n (4 n + 2 - n (n - 2) + 1 (n - 2))$

Step 9.2

Apply the distributive property.

$n (4 n + 2 - n \cdot n - n \cdot - 2 + 1 (n - 2))$

Step 9.3

Apply the distributive property.

$n (4 n + 2 - n \cdot n - n \cdot - 2 + 1 n + 1 \cdot - 2)$

Step 10

Simplify and combine like terms.

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Step 10.1

Simplify each term.

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Step 10.1.1

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

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Step 10.1.1.1

Move $n$ .

$n (4 n + 2 - (n \cdot n) - n \cdot - 2 + 1 n + 1 \cdot - 2)$

Step 10.1.1.2

Multiply $n$ by $n$ .

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

Step 10.1.2

Multiply $- 2$ by $- 1$ .

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

Step 10.1.3

Multiply $n$ by $1$ .

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

Step 10.1.4

Multiply $- 2$ by $1$ .

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

Step 10.2

Add $2 n$ and $n$ .

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

Step 11

Add $4 n$ and $3 n$ .

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

Step 12

Subtract $2$ from $2$ .

$n (7 n - n^{2} + 0)$

Step 13

Add $7 n - n^{2}$ and $0$ .

$n (7 n - n^{2})$

Step 14

Factor.

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Step 14.1

Factor $n$ out of $7 n - n^{2}$ .

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Step 14.1.1

Factor $n$ out of $7 n$ .

$n (n \cdot 7 - n^{2})$

Step 14.1.2

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

$n (n \cdot 7 + n (- n))$

Step 14.1.3

Factor $n$ out of $n \cdot 7 + n (- n)$ .

$n (n (7 - n))$

Step 14.2

Remove unnecessary parentheses.

$n \cdot n (7 - n)$

Step 15

Combine exponents.

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Step 15.1

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

$n^{1} n (7 - n)$

Step 15.2

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

$n^{1} n^{1} (7 - n)$

Step 15.3

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

$n^{1 + 1} (7 - n)$

Step 15.4

Add $1$ and $1$ .

$n^{2} (7 - n)$