Question

How to evaluate algebraic expressions

Answer 1

Evaluating algebraic expressions involves substituting specific values for the variables in the expression and then performing the arithmetic operations as indicated. Here’s a step-by-step guide on how to do it:

### Steps to Evaluate an Algebraic Expression

1. **Identify the Expression**: Start with the algebraic expression you need to evaluate. For example, let's say you have the expression \( 2x + 3y - 7 \).

2. **Substitute Values**: Determine the values for each variable in the expression. For example, if \( x = 4 \) and \( y = 2 \), substitute these values into the expression:
\[
2(4) + 3(2) - 7
\]

3. **Perform Arithmetic Operations**: Follow the order of operations (PEMDAS/BODMAS) to simplify the expression:
- **P/B**: Parentheses/Brackets
- **E/O**: Exponents/Orders
- **MD/DM**: Multiplication and Division (from left to right)
- **AS**: Addition and Subtraction (from left to right)

Continuing with the example:
\[
= 8 + 6 - 7
\]

4. **Combine Like Terms**: Perform the addition and subtraction:
\[
8 + 6 = 14
\]
Then,
\[
14 - 7 = 7
\]

5. **State the Result**: Write down the evaluated value. In this case, the expression \( 2x + 3y - 7 \) evaluates to \( 7 \) when \( x = 4 \) and \( y = 2 \).

### Example 2
Let’s evaluate another expression: \( a^2 - 4b + 6 \).
- Substitute \( a = 3 \) and \( b = 1 \):
\[
3^2 - 4(1) + 6
\]
- Then evaluate:
\[
= 9 - 4 + 6
\]
\[
= 5 + 6 = 11
\]
So, when \( a = 3 \) and \( b = 1 \), the expression evaluates to \( 11 \).

### Summary
- Identify the expression.
- Substitute values for variables.
- Follow the order of operations to calculate the result.
- Combine like terms and state the final answer.

This process can be applied to any algebraic expression; just ensure to follow the rules of arithmetic carefully.