Question

How do you simplify \[3{{q}^{2}}+q-{{q}^{2}}\]?

Answer 1

Hint: This type of problem is based on the concept of factorisation of a quadratic expression. First, we have to consider the given expression. Group all the \[{{q}^{2}}\] terms and add them. We get an expression with two terms. Since q is common in both the terms, we have to take q common out of the bracket. Make necessary calculations and convert the expression into a simplified form.

Complete step by step solution:
According to the question, we are asked to simplify \[3{{q}^{2}}+q-{{q}^{2}}\].
We have been given the expression is \[3{{q}^{2}}+q-{{q}^{2}}\]. --------(1)
First let us consider expression (1).
We find that the variable is q and the degree of the expression is 2.
Let us group all the \[{{q}^{2}}\] terms by rearranging the expression.
\[\Rightarrow 3{{q}^{2}}+q-{{q}^{2}}=3{{q}^{2}}-{{q}^{2}}+q\]
On taking \[{{q}^{2}}\] common from the first two terms, we get
\[3{{q}^{2}}+q-{{q}^{2}}={{q}^{2}}\left( 3-1 \right)+q\]
On further simplification, we get
\[\Rightarrow 3{{q}^{2}}+q-{{q}^{2}}=2{{q}^{2}}+q\]
Now, we have obtained an expression with two terms with variable q.
We know that \[{{q}^{2}}=q\times q\]. Thus, we can write the expression as
\[3{{q}^{2}}+q-{{q}^{2}}=2q\times q+q\]
We find that q is common in both the terms. On taking q common out of the bracket, we get
\[3{{q}^{2}}+q-{{q}^{2}}=q\left( 2q+1 \right)\]
We find that the expression cannot be simplified further.
Therefore, the simplified expression of \[3{{q}^{2}}+q-{{q}^{2}}\] is \[q\left( 2q+1 \right)\].

Note:
Whenever we get such types of problems, we have to look for the common terms and reduce the expression into a minimum number of terms. In this question, we should not simplify, take q common from the given expression and finalise the answer. Instead, we have to convert the equation into two terms and then take q common out of the bracket. Similarly, we can simplify the expressions with degree 3.