Simplify 3x(x-12x)+3x^2-2(x-2)^2

$3 x (x - 12 x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Simplify each term.

Subtract $12 x$ from $x$ .

$3 x (- 11 x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Rewrite using the commutative property of multiplication.

$3 \cdot - 11 x \cdot x + 3 x^{2} - 2 {(x - 2)}^{2}$

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

Move $x$ .

$3 \cdot - 11 (x \cdot x) + 3 x^{2} - 2 {(x - 2)}^{2}$

Multiply $x$ by $x$ .

$3 \cdot - 11 x^{2} + 3 x^{2} - 2 {(x - 2)}^{2}$

Multiply $3$ by $- 11$ .

$- 33 x^{2} + 3 x^{2} - 2 {(x - 2)}^{2}$

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

$- 33 x^{2} + 3 x^{2} - 2 ((x - 2) (x - 2))$

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x (x - 2) - 2 (x - 2))$

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x \cdot x + x \cdot - 2 - 2 (x - 2))$

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2)$

Move $- 2$ to the left of $x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2)$

Multiply $- 2$ by $- 2$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 2 x - 2 x + 4)$

Subtract $2 x$ from $- 2 x$ .

$- 33 x^{2} + 3 x^{2} - 2 (x^{2} - 4 x + 4)$

Apply the distributive property.

$- 33 x^{2} + 3 x^{2} - 2 x^{2} - 2 (- 4 x) - 2 \cdot 4$

Simplify.

Multiply $- 4$ by $- 2$ .

$- 33 x^{2} + 3 x^{2} - 2 x^{2} + 8 x - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$- 33 x^{2} + 3 x^{2} - 2 x^{2} + 8 x - 8$

Simplify by adding terms.

Add $- 33 x^{2}$ and $3 x^{2}$ .

$- 30 x^{2} - 2 x^{2} + 8 x - 8$

Subtract $2 x^{2}$ from $- 30 x^{2}$ .

$- 32 x^{2} + 8 x - 8$