Write as an Equation f(n)=(n-1)^2+3n

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

Step 1

Rewrite the function as an equation.

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

Step 2

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $n$ by $n$ .

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

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

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

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

Subtract $n$ from $- n$ .

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

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

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