Find the value of the algebraic expression 3x
3
y − 5x
2
y for x = −2 and y = −1.


To solve the algebraic expression \(3x^3y - 5x^2y\) for \(x = -2\) and \(y = -1\), follow these steps:

1. **Substitute the values of \(x = -2\) and \(y = -1\) into the expression**:
   \[
   3(-2)^3(-1) - 5(-2)^2(-1)
   \]

2. **Simplify each term**:

   - First term: 
     \[
     3(-2)^3(-1) = 3(-8)(-1) = 24
     \]
     
   - Second term: 
     \[
     5(-2)^2(-1) = 5(4)(-1) = -20
     \]

3. **Combine the results**:
   \[
   24 - (-20) = 24 + 20 = 44
   \]

So, the value of the expression is **44**.

Would you like further explanation or more details?

Here are 5 related questions you might find interesting:
1. How does changing the value of \(y\) affect the result?
2. What happens if both \(x\) and \(y\) are positive?
3. Can you explain the difference between powers with positive and negative bases?
4. How do the exponents affect the result in an algebraic expression?
5. Can this expression be factored in a more general form?

**Tip:** Always simplify expressions step by step, ensuring you apply correct operations, especially with negative signs!

Find the value of the algebraic expression 3x^3y − 5x^2y for x = −2 and y = −1.

Solve the algebraic expression 3x^3y − 5x^2y by substituting x = −2 and y = −1. This step-by-step guide demonstrates key algebraic concepts, including exponentiation, substitution, and simplifying polynomials. Suitable for students in Grades 8-10.

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