Sure, let's solve the expression [tex]\( a^2 - b^2 - 2bc - c^2 \)[/tex] step by step.
Let's assume the following values for the variables:
- [tex]\( a = 3 \)[/tex]
- [tex]\( b = 2 \)[/tex]
- [tex]\( c = 1 \)[/tex]
First, we evaluate each term in the expression:
1. Calculate [tex]\( a^2 \)[/tex]:
[tex]\[
a^2 = 3^2 = 9
\][/tex]
2. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = 2^2 = 4
\][/tex]
3. Calculate [tex]\( 2bc \)[/tex]:
[tex]\[
2bc = 2 \cdot 2 \cdot 1 = 4
\][/tex]
4. Calculate [tex]\( c^2 \)[/tex]:
[tex]\[
c^2 = 1^2 = 1
\][/tex]
Next, substitute these values into the expression:
[tex]\[
a^2 - b^2 - 2bc - c^2
\][/tex]
[tex]\[
= 9 - 4 - 4 - 1
\][/tex]
Finally, combine the terms:
[tex]\[
9 - 4 - 4 - 1 = 0
\][/tex]
So, the value of the expression [tex]\( a^2 - b^2 - 2bc - c^2 \)[/tex] when [tex]\( a = 3 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = 1 \)[/tex] is 0.
