Simplify 2-(3x-5)^2

$2 - {(3 x - 5)}^{2}$

Simplify each term.

Rewrite ${(3 x - 5)}^{2}$ as $(3 x - 5) (3 x - 5)$ .

$2 - ((3 x - 5) (3 x - 5))$

Expand $(3 x - 5) (3 x - 5)$ using the FOIL Method.

Apply the distributive property.

$2 - (3 x (3 x - 5) - 5 (3 x - 5))$

Apply the distributive property.

$2 - (3 x (3 x) + 3 x \cdot - 5 - 5 (3 x - 5))$

Apply the distributive property.

$2 - (3 x (3 x) + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 - (3 \cdot 3 x \cdot x + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 - (3 \cdot 3 (x \cdot x) + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5)$

Multiply $x$ by $x$ .

$2 - (3 \cdot 3 x^{2} + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5)$

Multiply $3$ by $3$ .

$2 - (9 x^{2} + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5)$

Multiply $- 5$ by $3$ .

$2 - (9 x^{2} - 15 x - 5 (3 x) - 5 \cdot - 5)$

Multiply $3$ by $- 5$ .

$2 - (9 x^{2} - 15 x - 15 x - 5 \cdot - 5)$

Multiply $- 5$ by $- 5$ .

$2 - (9 x^{2} - 15 x - 15 x + 25)$

Subtract $15 x$ from $- 15 x$ .

$2 - (9 x^{2} - 30 x + 25)$

Apply the distributive property.

$2 - (9 x^{2}) - (- 30 x) - 1 \cdot 25$

Simplify.

Multiply $9$ by $- 1$ .

$2 - 9 x^{2} - (- 30 x) - 1 \cdot 25$

Multiply $- 30$ by $- 1$ .

$2 - 9 x^{2} + 30 x - 1 \cdot 25$

Multiply $- 1$ by $25$ .

$2 - 9 x^{2} + 30 x - 25$

Subtract $25$ from $2$ .

$- 9 x^{2} + 30 x - 23$