Simplify 2x^2-(x-2y)(2x+y)

$2 x^{2} - (x - 2 y) (2 x + y)$

Simplify each term.

Apply the distributive property.

$2 x^{2} + (- x - (- 2 y)) (2 x + y)$

Multiply $- 2$ by $- 1$ .

$2 x^{2} + (- x + 2 y) (2 x + y)$

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

Apply the distributive property.

$2 x^{2} - x (2 x + y) + 2 y (2 x + y)$

Apply the distributive property.

$2 x^{2} - x (2 x) - x y + 2 y (2 x + y)$

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x^{2} - 1 \cdot 2 x \cdot x - x y + 2 y (2 x) + 2 y \cdot y$

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

Move $x$ .

$2 x^{2} - 1 \cdot 2 (x \cdot x) - x y + 2 y (2 x) + 2 y \cdot y$

Multiply $x$ by $x$ .

$2 x^{2} - 1 \cdot 2 x^{2} - x y + 2 y (2 x) + 2 y \cdot y$

Multiply $- 1$ by $2$ .

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

Rewrite using the commutative property of multiplication.

$2 x^{2} - 2 x^{2} - x y + 2 \cdot 2 y x + 2 y \cdot y$

Multiply $2$ by $2$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Add $- x y$ and $4 y x$ .

Move $y$ .

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

Add $- x y$ and $4 x y$ .

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

Simplify by adding terms.

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

$0 + 3 x y + 2 y^{2}$

Add $0$ and $3 x y$ .

$3 x y + 2 y^{2}$