Evaluate the expression:

[tex]\[ -a^2 - 2bc - |c| \][/tex]

Given:

[tex]\[ a = -3, \ b = -5, \ \text{and} \ c = 2 \][/tex]



Answer :

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].