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

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

Simplify each term.

Rewrite ${(2 x + y)}^{2}$ as $(2 x + y) (2 x + y)$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ .

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

Add $2 x y$ and $2 y x$ .

Move $y$ .

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

Add $2 x y$ and $2 x y$ .

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 2$ by $- 2$ .

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

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

Move $y$ .

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

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

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

Apply the distributive property.

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

Simplify.

Multiply $- 4$ by $- 1$ .

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

Multiply $4$ by $- 1$ .

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

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

Simplify by adding terms.

Subtract $x^{2}$ from $4 x^{2}$ .

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

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

$3 x^{2} + y^{2} + 8 x y - 4 y^{2}$

Subtract $4 y^{2}$ from $y^{2}$ .

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

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

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