When you simplify algebraic expressions with addition and subtraction, you're putting similar terms together. This is an important skill in Year 9 math and will help you with harder problems later on. Let's make this easy to understand.

What are Like Terms?

Like terms are terms that have the same variable and power.

For example, in the expression (3x + 5x), both parts have the variable (x) to the first power. That makes them like terms.

But (2x^2) and (3x) are not like terms because they have different powers of (x).

Steps to Simplify

1. Find Like Terms: Look for terms that can be added together.
2. Combine the Numbers: After finding the like terms, add or subtract their numbers.

Example 1

Take a look at this expression:

$3x + 4x - 2x$

Step 1: Find the like terms: (3x), (4x), and (-2x) are all like terms because they each have the variable (x).

Step 2: Add their numbers together:

$3 + 4 - 2 = 5$

So,

$3x + 4x - 2x = 5x$

Subtracting Expressions

When you need to subtract something, remember to distribute the negative sign to each part.

Example 2

Let's simplify this:

$5x + 3 - (2x + 4)$

Step 1: Distribute the negative sign:

$5x + 3 - 2x - 4$

Step 2: Combine like terms:

• For (x): (5x - 2x = 3x)
• For the numbers: (3 - 4 = -1)

So,

$5x + 3 - (2x + 4) = 3x - 1$

Summary

To sum it up, simplifying algebraic expressions using addition and subtraction means finding like terms and combining them. This skill not only makes expressions simpler but also helps you solve equations better. Enjoy simplifying!