Simplification of Brackets

Simplification and Brackets

To simplify an expression means to write it in a very neat way so it is easy to work with.

To simplify an expression means that you are writing an algebraic expression in a form that is easier to use if you want to do something else with the expression.

It means making a long math sentence look short and simple.

When we simplify brackets, we are opening them up by multiplying what is outside with what is inside.

Simplification of brackets in an expression implies the expansion of brackets.

It just means we remove the brackets by using multiplication.

We use a special rule called the distributive law to do this.

Distributive law means we use the distributive law of multiplication over addition or subtraction.

This rule tells us to share the number outside to everything inside the bracket.

Generally, it is written as:

x (y + z) = xy + xz

Example Expand and simplify the following

1. 9 (5 + 3)

2. 11 (2x + 3)

Solution 1

In this first question, the numbers 5 and 3 are like terms because they are both normal numbers.

We can solve this in two ways.

Method 1 Add the terms inside the bracket first, then multiply by the number outside.

9 (5 + 3) = 9 (8)

= 9 x 8

= 72

Method 2 Multiply the number outside with each term inside one by one, then add them.

9 (5 + 3) = (9 x 5) + (9 x 3)

= 45 + 27 = 72

Solution 2

In this second question, 2x and 3 are unlike terms because one has a letter and the other does not.

Since we cannot add them directly, we multiply the number outside by each term inside.

11 (2x + 3) = (11 x 2x) + (11 x 3)

= 22x + 33