SIMPLIFICATION OF EXPRESSIONS WITH

GROUPING SYMBOLSBY: MÓNICA ELIZONDO

YANN VILLARREAL

OBJECTIVES

• By the end of this lesson you should be able to:

• Simplify expressions through the removing of grouping symbols

SIMPLIFICATION OF ALGEBRAIC EXPRESSIONS

• Sometimes it is in an algebraic expression there is a group of terms that is grouped, because it is desired to be considered as a whole. For example, when we multiply two polynomials each one of them is enclosed by a pair of parenthesis in order to separate the terms of each one from the ones of the other.

• When grouping we use symbols like:

a) The parentheses ( )

b) The square brackets [ ]

c) The curly-braces { }

• In order to express an algebraic expression in a simplified way we have to remove all of the grouping symbols present on it. In order to do this we have to remove each pair of symbols one by one, starting from the most internal to the most external, and finally we have to perform the reduction of like terms (as we saw in the first topic of this module).

EXAMPLE

• Now we are going to practice with some examples.

Simplify the expression: 6𝑥 − [3 − (2 − 4𝑥)]

1. Identify the most internal pair of grouping symbols, in this case they are the parenthesis that sorrundsthe expression 2 − 4𝑥.

2. Now proceed to remove those symbols, this gives us of the expression: 6𝑥 − [3 − 2 + 4𝑥]

3. Repeat the steps 1 and 2 with the new expression, this gives us the expression 6𝑥 − 3 + 2 − 4𝑥

4. Finally, apply the reduction of like terms to the final expression obtained, this gives us the result: 2𝑥 −1

Solution: 2𝑥 − 1

PRACTICE!

• Now it’s time for you to practice, try the following problems. Simplify the following expressions:

a) 8𝑥 + 3 − 5x − 2 + 4x − 15

b) 2𝑥2 + 5𝑥 − 8 − [ 2𝑥 + 5 𝑥 + 3 − (𝑥2 − 6𝑥 + 1)]

ANSWERS

a) 8𝑥 + 3 − 5x − 2 + 4x − 15 = 20 − x

b) 2𝑥2 + 5𝑥 − 8 − 2𝑥 + 5 𝑥 + 3 − 𝑥2 − 6𝑥 + 1 = 𝑥2 + 8