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