Question

How do you simplify $2x+3y+2\left( x-y \right)-3x$ ?

Answer 1

Hint: We first need to apply distributive property to the brackets and then bring the $x$ terms together and the $y$ terms together. The simplification is then carried out by doing the additions and subtractions.

Complete step-by-step solution:
The given expression is
$2x+3y+2\left( x-y \right)-3x$
The third term is a bracket term. In order to simplify the expression we need to take out the terms within the brackets. This can be done by applying the distributive property to the bracket. The distributive property states that an expression of the type $a\left( b+c \right)$ can be written as $ab+bc$ . So, applying the distributive property to the expression, the expression thus becomes,
$\Rightarrow 2x+3y+2x-2y-3x$
If we observe closely, we can see that the expression consists of only two types of terms, terms containing $x$ and terms containing \[y\] . But, the terms are arranged haphazardly. We need to bring together the like terms by rearranging them. After rearranging, the expression thus becomes,
$\Rightarrow 2x+2x-3x+3y-2y$
Taking $x$ common from the first three terms, the expression becomes,
 $\Rightarrow \left( 2+2-3 \right)x+3y-2y$
Upon simplification, the expression becomes,
$\Rightarrow \left( 1 \right)x+3y-2y$
Taking $y$ common from the last two terms, we get,
$\Rightarrow x+\left( 3-2 \right)y$
Upon simplification, the expression becomes,
$\Rightarrow x+y$
Therefore, we can conclude that the given expression $2x+3y+2\left( x-y \right)-3x$ gets simplified to $x+y$.

Note: While simplifying an expression, we must always keep in mind the BODMAS rule. If there had been an expression which included terms other than $x$ and $y$ , then we must solve accordingly. We must simplify the expression to the greatest extent to which the individual $x$ and $y$ terms can get simplified.