Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(n + 1)}^{2}$ as $(n + 1) (n + 1)$ .

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $n$ by $n$ .

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

Step 1.3.1.2

Multiply $n$ by $1$ .

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

Step 1.3.1.3

Multiply $n$ by $1$ .

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

Step 1.3.1.4

Multiply $1$ by $1$ .

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

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

Step 1.3.2

Add $n$ and $n$ .

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

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

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

Step 2

Combine the opposite terms in $n^{2} + 2 n + 1 - n^{2}$ .

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Step 2.1

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

$2 n + 1 + 0$

Step 2.2

Add $2 n + 1$ and $0$ .

$2 n + 1$

$2 n + 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$