Sure, let's solve the expression [tex]\(-a^2 - 2bc - |c|\)[/tex] step by step, given that [tex]\(a = -3\)[/tex], [tex]\(b = -5\)[/tex], and [tex]\(c = 2\)[/tex].
1. Evaluate [tex]\(-a^2\)[/tex]:
[tex]\(a = -3\)[/tex]
[tex]\[
-a^2 = -(-3)^2 = -9
\][/tex]
So, [tex]\(-a^2 = -9\)[/tex].
2. Evaluate [tex]\(-2bc\)[/tex]:
[tex]\(b = -5\)[/tex] and [tex]\(c = 2\)[/tex]
[tex]\[
-2bc = -2 \times (-5) \times 2 = -2 \times -10 = 20
\][/tex]
So, [tex]\(-2bc = 20\)[/tex].
3. Evaluate [tex]\(-|c|\)[/tex]:
[tex]\(c = 2\)[/tex]
[tex]\[
|c| = |2| = 2
\][/tex]
[tex]\[
-|c| = -2
\][/tex]
So, [tex]\(-|c| = -2\)[/tex].
4. Combine the results:
Now, we add up the individual terms:
[tex]\[
-a^2 + (-2bc) + (-|c|) = -9 + 20 - 2
\][/tex]
Summing these values:
[tex]\[
-9 + 20 - 2 = 9
\][/tex]
So, the value of the expression [tex]\(-a^2 - 2bc - |c|\)[/tex] when [tex]\(a = -3\)[/tex], [tex]\(b = -5\)[/tex], and [tex]\(c = 2\)[/tex] is [tex]\(\boxed{9}\)[/tex].
