Question

How do you simplify \[\left[ {\left( {5 + 2} \right) - 3} \right]4\] ?

Answer 1

Hint: This question can be solved by using BODMAS rule, BODMAS stands for Brackets, of or order, Division, Multiplication, Addition, Subtraction.
Here the order is as follows:
Simplify the terms inside the parentheses or brackets, i.e., perform addition.
Next perform subtraction operation inside the brackets.
Finally perform the multiplication by releasing the brackets.

Complete step-by-step solution:
In mathematics, in order to evaluate an arithmetic expression that involves multiple operators such as division, addition, multiplication, subtraction, operator precedence (order of operations) is required which is a collection of rules that reflect conventions about which procedures to perform first. This is known as the BODMAS Rule.
The full form of “BODMAS” in Brackets, of or order, Division, Multiplication, Addition, Subtraction
What is the BODMAS Rule?
BODMAS is an acronym that stands for:
B = Brackets
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
After division and multiplication, we solve addition and subtraction from left to right in the given expression.
Now given expression is \[\left[ {\left( {5 + 2} \right) - 3} \right]4\] ,
Using BODMAS rule, first we have to solve the expression in \[\left( {} \right)\] ,i.e.,
 \[ \Rightarrow \left[ {\left( 7 \right) - 3} \right]4\] ,
Now again BODMAS rule we will perform subtraction operation, we get,
 \[ \Rightarrow \left[ {7 - 3} \right]4\] ,
Simplifying we get,
 \[ \Rightarrow \left[ 4 \right]4\] ,
Now releasing the brackets, or multiplying we get,
 \[ \Rightarrow 16\] ,
So \[\left[ {\left( {5 + 2} \right) - 3} \right]4\] \[ = 16\] .

\[\therefore \] The simplified form of the expression \[\left[ {\left( {5 + 2} \right) - 3} \right]4\] is 16.

Note: BODMAS explains the order of operations to solve an expression. According to the rule, if an expression consists of brackets \[\left( {\left( {} \right),\left[ {} \right],\left\{ {} \right\}} \right)\] we must solve or simplify the bracket followed by of powers and roots, then division, multiplication, addition and subtraction from left to right.
According to the BODMAS rules,
(I) B: Brackets \[\left( {\left( {} \right),\left[ {} \right],\left\{ {} \right\}} \right)\]
If an expression contains brackets we have to first simplify all these brackets.
(II) O: of or order (power or roots)
Followed by brackets, we solve “of” or “power” (square or roots) in the given expression.
(III) D: Division(“/”)
Then we solve division left to right in the given expression.
(IV) M: Multiplication(“*”)
After Division, we solve multiplication from left to right in the given expression.
(V) A: Addition(“+”)
(VI) S: Subtraction(“-“)