Evaluate the value of each of the following algebraic expressions if m= -2, e= -1, g= 3.  Evaluate: m²[8-(g-3e)²]

Let's evaluate the expression \( m^2[8 - (g - 3e)^2] \) using the given values \( m = -2 \), \( e = -1 \), and \( g = 3 \).

1. **Substitute the values into the expression**:
   \[
   (-2)^2 \left[ 8 - \left(3 - 3(-1)\right)^2 \right]
   \]

2. **Simplify the expression inside the brackets**:
   \[
   3 - 3(-1) = 3 + 3 = 6
   \]
   So, the expression becomes:
   \[
   (-2)^2 \left[ 8 - (6)^2 \right]
   \]

3. **Square the values**:
   \[
   (-2)^2 = 4
   \]
   \[
   (6)^2 = 36
   \]
   Now, the expression is:
   \[
   4 \left[ 8 - 36 \right]
   \]

4. **Subtract inside the brackets**:
   \[
   8 - 36 = -28
   \]
   The expression now is:
   \[
   4(-28)
   \]

5. **Multiply**:
   \[
   4 \times -28 = -112
   \]

Thus, the value of the expression \( m^2[8 - (g - 3e)^2] \) is \( \boxed{-112} \).

Would you like a detailed explanation of any step? Here are some related questions you might find interesting:

1. How do you simplify expressions with multiple variables?
2. What is the importance of order of operations in algebra?
3. How do you handle negative exponents in algebraic expressions?
4. What are some common mistakes to avoid when evaluating algebraic expressions?
5. How does squaring a negative number affect the overall expression?

**Tip:** Always carefully substitute values and follow the order of operations (PEMDAS) to avoid errors when evaluating expressions.

Learn how to evaluate the algebraic expression m²[8-(g-3e)²] using specific values for m, e, and g. Follow a step-by-step solution to understand exponentiation and order of operations in algebra. Suitable for students in Grades 7-9.

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