Write in Standard Form y=(-3x)^2-3(x-3)^2

$y = {(- 3 x)}^{2} - 3 {(x - 3)}^{2}$

Step 1

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

$y = a x^{2} + b x + c$

Step 2

Simplify each term.

Apply the product rule to $- 3 x$ .

$y = {(- 3)}^{2} x^{2} - 3 {(x - 3)}^{2}$

Raise $- 3$ to the power of $2$ .

$y = 9 x^{2} - 3 {(x - 3)}^{2}$

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$y = 9 x^{2} - 3 ((x - 3) (x - 3))$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$y = 9 x^{2} - 3 (x (x - 3) - 3 (x - 3))$

Apply the distributive property.

$y = 9 x^{2} - 3 (x \cdot x + x \cdot - 3 - 3 (x - 3))$

Apply the distributive property.

$y = 9 x^{2} - 3 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 9 x^{2} - 3 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3)$

Move $- 3$ to the left of $x$ .

$y = 9 x^{2} - 3 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3)$

Multiply $- 3$ by $- 3$ .

$y = 9 x^{2} - 3 (x^{2} - 3 x - 3 x + 9)$

Subtract $3 x$ from $- 3 x$ .

$y = 9 x^{2} - 3 (x^{2} - 6 x + 9)$

Apply the distributive property.

$y = 9 x^{2} - 3 x^{2} - 3 (- 6 x) - 3 \cdot 9$

Simplify.

Multiply $- 6$ by $- 3$ .

$y = 9 x^{2} - 3 x^{2} + 18 x - 3 \cdot 9$

Multiply $- 3$ by $9$ .

$y = 9 x^{2} - 3 x^{2} + 18 x - 27$

Step 3

Subtract $3 x^{2}$ from $9 x^{2}$ .

$y = 6 x^{2} + 18 x - 27$

Step 4