To solve the expression [tex]\(2x^2 - 5xy - y^3\)[/tex] using the given values [tex]\(x = -3\)[/tex] and [tex]\(y = -2\)[/tex], let us break it down into several steps:
1. Calculate the term [tex]\(2x^2\)[/tex]:
[tex]\[
x = -3 \\
x^2 = (-3)^2 = 9 \\
2x^2 = 2 \times 9 = 18
\][/tex]
So, the value of [tex]\(2x^2\)[/tex] is 18.
2. Calculate the term [tex]\(-5xy\)[/tex]:
[tex]\[
x = -3 \quad \text{and} \quad y = -2 \\
xy = (-3) \times (-2) = 6 \\
-5xy = -5 \times 6 = -30
\][/tex]
So, the value of [tex]\(-5xy\)[/tex] is -30.
3. Calculate the term [tex]\(-y^3\)[/tex]:
[tex]\[
y = -2 \\
y^3 = (-2)^3 = -8 \\
-y^3 = -(-8) = 8
\][/tex]
So, the value of [tex]\(-y^3\)[/tex] is 8.
4. Combine all the calculated terms:
[tex]\[
2x^2 - 5xy - y^3 = 18 - 30 + 8
\][/tex]
5. Perform the final addition and subtraction:
[tex]\[
18 - 30 + 8 = -12 + 8 = -4
\][/tex]
Hence, the value of the expression [tex]\(2x^2 - 5xy - y^3\)[/tex] when [tex]\(x = -3\)[/tex] and [tex]\(y = -2\)[/tex] is [tex]\(\boxed{-4}\)[/tex].
The intermediate values are:
- The term [tex]\(2x^2\)[/tex] is 18.
- The term [tex]\(-5xy\)[/tex] is -30.
- The term [tex]\(-y^3\)[/tex] is 8.
- The result of the expression is -4.
