Write in Standard Form f(x)=5(x-1)^2-5

$f (x) = 5 {(x - 1)}^{2} - 5$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify each term.

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

$f (x) = 5 ((x - 1) (x - 1)) - 5$

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

Apply the distributive property.

$f (x) = 5 (x (x - 1) - 1 (x - 1)) - 5$

Apply the distributive property.

$f (x) = 5 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 5$

Apply the distributive property.

$f (x) = 5 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = 5 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 5$

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

$f (x) = 5 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 5$

Rewrite $- 1 x$ as $- x$ .

$f (x) = 5 (x^{2} - x - 1 x - 1 \cdot - 1) - 5$

Rewrite $- 1 x$ as $- x$ .

$f (x) = 5 (x^{2} - x - x - 1 \cdot - 1) - 5$

Multiply $- 1$ by $- 1$ .

$f (x) = 5 (x^{2} - x - x + 1) - 5$

Subtract $x$ from $- x$ .

$f (x) = 5 (x^{2} - 2 x + 1) - 5$

Apply the distributive property.

$f (x) = 5 x^{2} + 5 (- 2 x) + 5 \cdot 1 - 5$

Simplify.

Multiply $- 2$ by $5$ .

$f (x) = 5 x^{2} - 10 x + 5 \cdot 1 - 5$

Multiply $5$ by $1$ .

$f (x) = 5 x^{2} - 10 x + 5 - 5$

Step 3

Combine the opposite terms in $5 x^{2} - 10 x + 5 - 5$ .

Subtract $5$ from $5$ .

$f (x) = 5 x^{2} - 10 x + 0$

Add $5 x^{2} - 10 x$ and $0$ .

$f (x) = 5 x^{2} - 10 x$