Write in Standard Form -3(y+2)^2-5+6y

$- 3 {(y + 2)}^{2} - 5 + 6 y$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Simplify each term.

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

$- 3 ((y + 2) (y + 2)) - 5 + 6 y$

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

Apply the distributive property.

$- 3 (y (y + 2) + 2 (y + 2)) - 5 + 6 y$

Apply the distributive property.

$- 3 (y \cdot y + y \cdot 2 + 2 (y + 2)) - 5 + 6 y$

Apply the distributive property.

$- 3 (y \cdot y + y \cdot 2 + 2 y + 2 \cdot 2) - 5 + 6 y$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$- 3 (y^{2} + y \cdot 2 + 2 y + 2 \cdot 2) - 5 + 6 y$

Move $2$ to the left of $y$ .

$- 3 (y^{2} + 2 \cdot y + 2 y + 2 \cdot 2) - 5 + 6 y$

Multiply $2$ by $2$ .

$- 3 (y^{2} + 2 y + 2 y + 4) - 5 + 6 y$

Add $2 y$ and $2 y$ .

$- 3 (y^{2} + 4 y + 4) - 5 + 6 y$

Apply the distributive property.

$- 3 y^{2} - 3 (4 y) - 3 \cdot 4 - 5 + 6 y$

Simplify.

Multiply $4$ by $- 3$ .

$- 3 y^{2} - 12 y - 3 \cdot 4 - 5 + 6 y$

Multiply $- 3$ by $4$ .

$- 3 y^{2} - 12 y - 12 - 5 + 6 y$

Simplify by adding terms.

Add $- 12 y$ and $6 y$ .

$- 3 y^{2} - 6 y - 12 - 5$

Subtract $5$ from $- 12$ .

$- 3 y^{2} - 6 y - 17$