# Simplify Algebraic Expressions

To simplify algebraic expressions, we collect or group **like terms**.

## Example One - Wildlife Reserve

Imagine a wildlife reserve has antelopes, gorillas, kangaroos and zebras.

Let each animal be identified using a letter such a, g, k, z.

**Question 1**

In one park of the wildlife reserve, there are 3 zebras, 5 gorillas and 6 kangaroos. A year later, 2 zebras and 3 gorillas are born, but 4 kangaroos died. How many of each animal are there now?

**Answer 1**

The like terms are the zebras, the gorillas and the kangaroos.

3z + 5g + 6k + 2z + 3g – 4k

= 5z + 8g + 2k

**Question 2**

In another part of the reserve, there are 2 kangaroos and 5 antelopes. After one year, the population of each group doubled. How many of each are there now?

**Answer 2**

The like terms are the antelopes and the kangaroos.

(2k + 5a) × 2

= 4k + 10a

## Example Two - Simplifying Algebraic Expressions

However, variables represent numbers not animals.

**Question 3**

Simplify 5a + 2a – 2c + 5 + 4b + 3b + 4a – c

**Answer 3**

5a + 2a – 2c + 5 + 4b + 3b + 4a – c

= 5a + 2a + 4a + 4b + 3b – 2c – c + 5

= 11a + 7b – 3c + 5

**Question 4**

Simplify 3a × 4 + 5b × 2 – 7c × 8

**Answer 4**

3a × 4 + 5b × 2 – 7c × 8

= 12a + 10b – 56c

## Questions

Simplify the following expressions.

**Q1.** 3a – 7b + 9 + 3a – a + 5c – 7c

**Q2.** 4g × 3 – 5h × 2 – 7f

**Answers**

**A1.** 5a – 7b – 2c + 9

**A2.** 12g – 10h – 7f