Brackets in computation

Brackets in Computation

Brackets are used to group items, and these items inside the brackets are considered as a whole. For example, $15 \div (x + 2)$ means that $x$ and 2 are added first and their sum should divide 15. If we are given an expression with mixed operations, the following order is used to perform the operations: Brackets (B) are opened first, followed by Division (D), then Multiplication (M), Addition (A) and lastly Subtraction (S). Shortly written as BODMAS.

Basic Operations Involving Brackets

Example 1

Simplify the following expressions:

1. $4 + 2b - (9b \div 3b)$
2. $4z - (2x + z)$

Solution

Example 2

Evaluate the following expressions:

Solution

Identities

For example, $3(2y + 3) = 6y + 9$, when $y = 1$, the right-hand side (RHS) and the left-hand side (LHS) are both equal to 15. If we substitute any other value, we obtain the same value on both sides. Therefore, the equations which are true for all values of the variables on both sides are called Identities. We can determine whether an equation is an identity or not by showing that an expression on one side is identical to the other expression on the other side.

Example 3

Determine whether or not the following expressions are identities:

Solution