To simplify the expression [tex]\(-3(y+2)^2 - 5 + 6y\)[/tex], you can follow these detailed steps:
1. Expand the squared binomial [tex]\((y + 2)^2\)[/tex] first:
[tex]\[
(y + 2)^2 = y^2 + 4y + 4
\][/tex]
2. Distribute [tex]\(-3\)[/tex] across the expanded binomial:
[tex]\[
-3(y^2 + 4y + 4) = -3y^2 - 12y - 12
\][/tex]
3. Combine the distributed terms with the rest of the expression:
[tex]\[
-3y^2 - 12y - 12 - 5 + 6y
\][/tex]
4. Simplify the expression by combining like terms:
[tex]\[
-3y^2 - 12y + 6y - 12 - 5
\][/tex]
[tex]\[
-3y^2 - 6y - 17
\][/tex]
Thus, the simplified expression in standard form is:
[tex]\[
-3y^2 - 6y - 17
\][/tex]
So, filling in the blanks in the standard form [tex]\(\square y^2 + \square y + \square\)[/tex], we have:
[tex]\[
-3y^2 + (-6)y + (-17)
\][/tex]
Hence, the answer is:
[tex]\[
-3, -6, -17
\][/tex]
