Question

How do you simplify $\left( 5p-3q \right)-\left( -3p+7q \right)$ ?

Answer 1

Hint: We can easily solve problems on simplifying an expression by using simple concepts of numbers written in algebraic forms. We must start simplifying the given expression by omitting the brackets applying the distributive property of numbers. Upon using the distributive property, we multiply $\left( -1 \right)$ to both the terms $-3p$ and $7q$ of the given expression. After doing that we combine the terms associated to $p$ and $q$ separately and further add them to get a simplified form of the given expression.

Complete step by step answer:
The expression we have is
 $\left( 5p-3q \right)-\left( -3p+7q \right)$
The above algebraic equation has two variables such as $p$ and $q$ .
To simplify the given expression, we must use simple concepts of numbers written in algebraic form.
The bracket around the term $\left( 5p-3q \right)$ can be easily neglected as there is nothing outside the bracket to be multiplied.
Hence, neglecting the bracket at first, we rewrite the given expression as
$=5p-3q-\left( -3p+7q \right)$
Now, in the above expression we can see that there is a negative sign outside the bracket which can be taken care of using the distributive property as shown below
 $=5p-3q+3p-7q$
Now, we combine the terms associated to $p$ as
$=\left( 5p+3p \right)-3q-7q$
Again, we take a $\left( -1 \right)$ common from the terms associated to $q$ as shown below
$=\left( 5p+3p \right)-\left( 3q+7q \right)$
We know that in algebraic expressions we can add the like terms.
Hence, we add the terms associated to $p$ and the terms associated to $q$ separately as
$=8p-10q$
Therefore, the simplified form of the expression $\left( 5p-3q \right)-\left( -3p+7q \right)$ is $8p-10q$ .

Note:
While using the distributive property, we must keep in mind that we must also take care of the sign of the number that is to be distributed so that the result we get becomes accurate. Also, we have to be careful while adding the like terms, as we often get confused between the variables and make mistakes in the solution.