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How do you simplify \[\left( 3a+4b \right)-\left( -6a-3b \right)\]?

seo-qna
Last updated date: 17th Jul 2024
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Answer
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Hint: We are given to solve \[\left( 3a+4b \right)-\left( -6a-3b \right)\]. For that first of all consider the given equation as equation (1) for a reference and then pull out the brackets from the equation and then add or subtract the terms. By simplifying the equation we will get the required answer.

Complete step by step solution:
For the given question we are given to solve the equation\[\left( 3a+4b \right)-\left( -6a-3b \right)\]. For that let us consider the equation as equation (1). Let us denote the given equation as equation ‘S’.
By denoting the equation with ‘S’, we get
\[S=\left( 3a+4b \right)-\left( -6a-3b \right)\]
 Let us consider the above equation as equation (1), we get
\[S=\left( 3a+4b \right)-\left( -6a-3b \right).......\left( 1 \right)\]
As we know that when minus sign is multiplied with minus sign we get minus, when minus sign is multiplied with addition sign we get minus, when addition sign is multiplied with addition sign we get addition sign. We have to apply these operations to simplify the equation (1).
Let us remove the brackets in equation (1), we get
 \[\Rightarrow S=3a+4b+6a+3b\]
Let us consider it as equation (2), we get
\[\Rightarrow S=3a+4b+6a+3b.........\left( 2 \right)\]
Now you can add or subtract together for any similar terms that have the same variables.
\[\Rightarrow S=9a+7b\]
Let us consider the above equation as equation (3), we get
\[\Rightarrow S=9a+7b.............\left( 3 \right)\]
This is the simplest form of given expression.

Note: For this type of problems we have to use BODMAS rule trick i.e. brackets open division addition subtraction. Which means first of the problem we have to open the brackets first and then we have to do the operations in order.