Question

How do you combine like terms in $5m\left( m+5 \right)-2+4\left( m-6 \right)$?

Answer 1

Hint: From the question we have been asked to combine the like terms in $5m\left( m+5 \right)-2+4\left( m-6 \right)$. For this question we will expand the terms inside the brackets using multiplication with the terms outside the brackets. By doing the multiplication next we will add the terms of same degree and simplify them. In this way we will solve the questions.

Complete step by step solution:
Firstly, we will use the basic mathematical operation which is multiplication and simplify the terms \[m+2\] and \[m-6\] by multiplying them with \[5m\] and 4 respectively.
So, in the first case we will expand the term \[m+2\]. So, the equation will be reduced as follows.
\[\Rightarrow 5m\left( m+5 \right)-2+4\left( m-6 \right)\]
\[\Rightarrow 5{{m}^{2}}+25m-2+4\left( m-6 \right)\]
Now, we will expand the other term. So, the equation will be further reduced as follows.
\[\Rightarrow 5{{m}^{2}}+25m-2+4\left( m-6 \right)\]
\[\Rightarrow 5{{m}^{2}}+25m-2+4m-24\]
Here in the question we have been asked to combine the like terms. So, we will rearrange the terms which we got in the equation. So, after rearranging we get the reduced as follows.
\[\Rightarrow 5{{m}^{2}}+25m-2+4m-24\]
\[\Rightarrow 5{{m}^{2}}+25m+4m-24-2\]
Here we will use the basic operation which is addition and simplify the equation. So we get the equation simplified as follows.
\[\Rightarrow 5{{m}^{2}}+25m+4m-24-2\]
\[\Rightarrow 5{{m}^{2}}+29m-26\]
Therefore, the solution for the given question will be \[ 5{{m}^{2}}+29m-26\].

Note: Students must be very careful in doing the calculations. Students should perform the basic operations which are multiplication and addition without any mistake. Here we should add only like terms in these questions we should not do mistakes like adding the unlike terms each other for example in this expression \[\Rightarrow 5{{m}^{2}}+25m+4m-24-2\] we should not add \[5{{m}^{2}}\] and \[29m\] which makes our solution a wrong. So, we must be careful in this aspect of the question.