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# How do you simplify $5\left( 3m-6 \right)$?

Last updated date: 13th Jun 2024
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Hint: In this problem we need to simplify the given expression i.e., we need to find the product of the given expression. For this we will multiply each term individually. First, we will multiply the terms $5$, $3m$ and then we will multiply the terms $5$, $-6$. Now we will add the two results to get the required result.

Complete step by step solution:
Given that, $5\left( 3m-6 \right)$.
Considering the terms $5$, $3m$. Now the product of the two terms $5$, $3m$ is given by
$5\times 3m=15m$
Considering the terms $5$, $-6$. Now the product of the two terms $5$, $-6$ is given by
$5\times -6=-30$
Now the sum of the results of the above two steps is given by
$15m+\left( -30 \right)=15m-30$.

Hence the product of the given equation $5\left( 3m-6 \right)$ is $15m-30$.

Note: For this problem we can use the distribution law of multiplication over the subtraction to get the result. The distribution law of multiplication over subtraction says that the product of the equation $a\left( b-c \right)$ is given by $a\left( b-c \right)=ab-ac$. So, we will compare the given equation with $a\left( b-c \right)$ and we will write the values of $a$, $b$, $c$. After knowing the values of $a$, $b$, $c$ we will calculate the values of $ab$, $ac$. After calculating the values of $ab$, $ac$, we will substitute those in the formula $a\left( b-c \right)=ab-ac$ to get the required result. The above procedure is somewhat lengthy so we haven’t used it in the solution.