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# How do you simplify $(2\times 3+2)+(5\times 3+3)$?

Last updated date: 05th Mar 2024
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Hint: In this question we have the expression which we will solve in the sequence of $PEMDAS$ which is an abbreviation for the term parenthesis, exponent, multiplication, division, addition and subtraction. Which is a sequence which we will use for simplifying the given linear expression and getting the required solution.

We have the given expression as:
$\Rightarrow (2\times 3+2)+(5\times 3+3)\to (1)$
Now from the $PEMDAS$ rule, we will first solve the parenthesis in the expression first.
Now consider the first term in the expression which is $(2\times 3+2)\to (1)$.
$\Rightarrow (2\times 3+2)$
Now in this bracket we have two operations which are multiplication and addition. By following the rule of $PEMDAS$, we can see that the priority of multiplication is greater than addition therefore, on multiplying the terms, we get:
$\Rightarrow (6+2)$
Now on adding the terms, we get:
$\Rightarrow 8$, which is the solution for the first part of the expression.
Now consider the second term in the expression which is $(5\times 3+3)\to (2)$.
$\Rightarrow (5\times 3+3)$
Now similarly, in this bracket we have two operations which are multiplication and addition. By following the rule of $PEMDAS$, we can see that the priority of multiplication is greater than addition therefore, on multiplying the terms, we get:
$\Rightarrow (15+3)$
Now on adding the terms, we get:
$\Rightarrow 18$, which is the solution
Now on adding equations $(2)$ and $(3)$, we get equation $(1)$ therefore, we can write the expression in the simplified manner as:
$\Rightarrow 8+18$
On simplifying the terms, we get:
$\Rightarrow 26$, which is the required solution.

Note: There is also another sequence of operation which is called $BODMAS$ which is the abbreviation for bracket order division, multiplication, addition and subtraction. The difference between $BODMAS$ and $PEMDAS$ is the order for division and multiplication. When these cases arise, the expression should be validated from left to right.