Basic Math Examples

$(1 + 2 n^{2}) - (2 - 2 n^{2})$

Step 1

Apply the distributive property.

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

Step 2

Multiply $- 1$ by $2$ .

$1 + 2 n^{2} - 2 - (- 2 n^{2})$

Step 3

Multiply $- 2$ by $- 1$ .

$1 + 2 n^{2} - 2 + 2 n^{2}$

Step 4

Subtract $2$ from $1$ .

$2 n^{2} - 1 + 2 n^{2}$

Step 5

Add $2 n^{2}$ and $2 n^{2}$ .

$4 n^{2} - 1$

Step 6

Rewrite $4 n^{2} - 1$ in a factored form.

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Step 6.1

Rewrite $4 n^{2}$ as ${(2 n)}^{2}$ .

${(2 n)}^{2} - 1$

Step 6.2

Rewrite $1$ as $1^{2}$ .

${(2 n)}^{2} - 1^{2}$

Step 6.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 n$ and $b = 1$ .

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