Algebra Examples

$f (n) = {(n - 1)}^{2} + 3 n$

Step 1

Rewrite the function as an equation.

$y = {(n - 1)}^{2} + 3 n$

Step 2

Simplify ${(n - 1)}^{2} + 3 n$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$y = (n - 1) (n - 1) + 3 n$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Apply the distributive property.

$y = n (n - 1) - 1 (n - 1) + 3 n$

Step 2.1.2.2

Apply the distributive property.

$y = n \cdot n + n \cdot - 1 - 1 (n - 1) + 3 n$

Step 2.1.2.3

Apply the distributive property.

$y = n \cdot n + n \cdot - 1 - 1 n - 1 \cdot - 1 + 3 n$

$y = n \cdot n + n \cdot - 1 - 1 n - 1 \cdot - 1 + 3 n$

Step 2.1.3

Simplify and combine like terms.

Tap for more steps...

Step 2.1.3.1

Simplify each term.

Tap for more steps...

Step 2.1.3.1.1

Multiply $n$ by $n$ .

$y = n^{2} + n \cdot - 1 - 1 n - 1 \cdot - 1 + 3 n$

Step 2.1.3.1.2

Move $- 1$ to the left of $n$ .

$y = n^{2} - 1 \cdot n - 1 n - 1 \cdot - 1 + 3 n$

Step 2.1.3.1.3

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

$y = n^{2} - n - 1 n - 1 \cdot - 1 + 3 n$

Step 2.1.3.1.4

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

$y = n^{2} - n - n - 1 \cdot - 1 + 3 n$

Step 2.1.3.1.5

Multiply $- 1$ by $- 1$ .

$y = n^{2} - n - n + 1 + 3 n$

$y = n^{2} - n - n + 1 + 3 n$

Step 2.1.3.2

Subtract $n$ from $- n$ .

$y = n^{2} - 2 n + 1 + 3 n$

$y = n^{2} - 2 n + 1 + 3 n$

$y = n^{2} - 2 n + 1 + 3 n$

Step 2.2

Add $- 2 n$ and $3 n$ .

$y = n^{2} + n + 1$

$y = n^{2} + n + 1$

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