Simplify (2y+1)^2-4y^2+2

${(2 y + 1)}^{2} - 4 y^{2} + 2$

Simplify each term.

Rewrite ${(2 y + 1)}^{2}$ as $(2 y + 1) (2 y + 1)$ .

$(2 y + 1) (2 y + 1) - 4 y^{2} + 2$

Expand $(2 y + 1) (2 y + 1)$ using the FOIL Method.

Apply the distributive property.

$2 y (2 y + 1) + 1 (2 y + 1) - 4 y^{2} + 2$

Apply the distributive property.

$2 y (2 y) + 2 y \cdot 1 + 1 (2 y + 1) - 4 y^{2} + 2$

Apply the distributive property.

$2 y (2 y) + 2 y \cdot 1 + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 y \cdot y + 2 y \cdot 1 + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

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

Move $y$ .

$2 \cdot 2 (y \cdot y) + 2 y \cdot 1 + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

Multiply $y$ by $y$ .

$2 \cdot 2 y^{2} + 2 y \cdot 1 + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

Multiply $2$ by $2$ .

$4 y^{2} + 2 y \cdot 1 + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

Multiply $2$ by $1$ .

$4 y^{2} + 2 y + 1 (2 y) + 1 \cdot 1 - 4 y^{2} + 2$

Multiply $2 y$ by $1$ .

$4 y^{2} + 2 y + 2 y + 1 \cdot 1 - 4 y^{2} + 2$

Multiply $1$ by $1$ .

$4 y^{2} + 2 y + 2 y + 1 - 4 y^{2} + 2$

Add $2 y$ and $2 y$ .

$4 y^{2} + 4 y + 1 - 4 y^{2} + 2$

Simplify by adding terms.

Combine the opposite terms in $4 y^{2} + 4 y + 1 - 4 y^{2} + 2$ .

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

$4 y + 1 + 0 + 2$

Add $4 y + 1$ and $0$ .

$4 y + 1 + 2$

Add $1$ and $2$ .

$4 y + 3$