Simplify 2x^2+4x-3(x-x^2)+(x+2)(x-2)

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $- 3$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Combine the opposite terms in $x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$ .

Reorder the factors in the terms $x \cdot - 2$ and $2 x$ .

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

Add $- 2 x$ and $2 x$ .

$2 x^{2} + 4 x - 3 x + 3 x^{2} + x \cdot x + 0 + 2 \cdot - 2$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 2$ .

$2 x^{2} + 4 x - 3 x + 3 x^{2} + x^{2} - 4$

Simplify by adding terms.

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

$5 x^{2} + 4 x - 3 x + x^{2} - 4$

Add $5 x^{2}$ and $x^{2}$ .

$6 x^{2} + 4 x - 3 x - 4$

Subtract $3 x$ from $4 x$ .

$6 x^{2} + x - 4$