What does double bracket mean in math?

What does double bracket mean in math?

Double brackets in math are used to solve when two expressions that are separated by round brackets are multiplied together. For example, if we wish multiply 3x + 8 and 8y + 9 we can write it as ( 3x + 8 ) ( 8y + 9 ).  So, we can say that, if we have two expressions, ( a + b ) and ( p + q ) and we need to find their product, then, using double brackets they can be written as

Before we understand how to solve such expressions, let us understand what brackets are.

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Using Brackets to Perform Mathematical operations

Various operations are performed in math using the four mathematical operators, namely addition, subtraction, multiplication and division. For example, 2 x 3 + 6 will be equal to 6 + 6 = 12.

However, there are many instances where we need to find the values equations or algebraic expressions that involve a number of mathematical operations. In such cases, we make use of brackets to define the order in which the operations need to be performed. Let us understand the type of brackets that are commonly used.

Types of brackets in math

There are four main types of brackets that are commonly used in various mathematical operations. These are –

• Parenthesis or Round Brackets ( ) – These brackets are used to group numbers and for performing various operations such as multiplication and division. Example, 2x + 6 can also be written as ( 2x + 6 )

• Curly Brackets { } – Curly brackets are the brackets that are generally used when we need more than one type of bracket for solving mathematical operations. Curly brackets are also known as Braces. For example, If we wish to add the result of ( 2x + 6 ) to the expression, ( 3y + 7 ), we can write the expression as

{ ( 2x + 6 ) + ( 3y + 7 ) }

• Square Brackets [ ] – The square brackets are the next in order for solving mathematical operations. They make it easier to understand the order of operations in the case of solving equations, especially those that involve algebraic expressions. For example, the expression 6 + 3  – 5 ÷ 10 x 3 can also be written as 

[ ( 6 + 3 ) – { 5 ÷ ( 10 x 3 ) } ]

• Angular Brackets < > These brackets are used to denote less than or greater than when comparing two numbers or variables. For example, x > 7 would mean that x can assume any value that is greater than 7.

Now, let us learn what does double brackets mean in math.

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How to solve double brackets in math?

As defined above double brackets come into use when we need to multiply two expressions. Let us take an example,

Example

Solve ( 2p + 7 ) ( 4p + 9 )

Solution

We can see that in the given question, there is a use of double brackets to represent the multiplication of two algebraic expressions. The double brackets here mean that

( 2p + 7 ) ( 4p + 9 )= ( 2p + 7 ) x ( 4p + 9 )

So, we have,

( 2p + 7 ) x ( 4p + 9 )

= 2p ( 4p + 9 ) + 7 ( 4p + 9 )

= 8p² + 18p + 28p + 63

= 8p² + 46p + 63

Hence, ( 2p + 7 ) ( 4p + 9 ) = 8p² + 46p + 63

So, we can define the general formula of solving double bracket in math as –

The steps to solve the double brackets can now be listed as

• The first value in the first expression is multiplied by all the values of the second expression.
• This is followed by the operator that lies next to the first expression.
• Then the second value in the first expression is multiplied by all the values of the second expression.
• This process is carried on until the end of the first expression is reached.

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