Question

How can you add and subtract algebraic expressions?

Answer 1

Adding and subtracting algebraic expressions involves combining like terms, which are terms that have the same variable raised to the same power. Here’s a step-by-step guide:

### Adding Algebraic Expressions

1. **Identify Like Terms**: Look for terms in the expressions that have the same base and exponent. For example, in the expression \(3x^2 + 5x^2\), both terms are like terms because they both contain \(x^2\).

2. **Combine Like Terms**: Add the coefficients of the like terms together. Using the previous example:
\[
3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2
\]

3. **Rewrite the Expression**: Write the new expression with the combined like terms. Include any other terms that weren't like terms.
- For instance, if you have \(2x + 3 + 4x^2 + 1\):
\[
2x + 4x^2 + (3 + 1) = 4x^2 + 2x + 4
\]

### Subtracting Algebraic Expressions

1. **Distribute the Negative Sign**: When you subtract an algebraic expression, first distribute the negative sign (or the subtraction) across the entire expression you are subtracting. For instance:
\[
5x + 3 - (2x + 1) = 5x + 3 - 2x - 1
\]

2. **Combine Like Terms**: Just as with addition, combine the like terms.
- From the previous step:
\[
(5x - 2x) + (3 - 1) = 3x + 2
\]

3. **Rewrite the Expression**: Write the new expression clearly.
- The result is \(3x + 2\).

### Examples

1. **Addition Example**:
\[
(2x + 3) + (4x - 5) = 2x + 4x + 3 - 5 = 6x - 2
\]

2. **Subtraction Example**:
\[
(3y^2 + 4y) - (2y^2 + 5y) = 3y^2 - 2y^2 + 4y - 5y = (3 - 2)y^2 + (4 - 5)y = y^2 - y
\]

### Summary

To add or subtract algebraic expressions:

- Combine like terms by adding or subtracting their coefficients.
- Be careful when distributing the negative sign during subtraction.
- Write your final expression neatly, ensuring all like terms are combined correctly.