Question

How do you simplify $6\left( -5n+7 \right)$?

Answer 1

Hint: In this problem we need to simplify the given value. For this we are going to use the distribution law of multiplication. Distribution law of multiplication says that the value of $a\left( b\pm c \right)$ will be $ab\pm ac$, mathematically it can be written as $a\left( b\pm c \right)=ab\pm ac$. So, we will compare the given value with $a\left( b\pm c \right)$ and write the values of $a$, $b$, $c$. After that we will calculate the values of $ab$, $ac$. Now we will substitute those values in the formula to get the required result.

Complete step by step solution:
Given that, $6\left( -5n+7 \right)$.
Comparing the above given value with $a\left( b+c \right)$, then we will get the values of $a$, $b$, $c$ as
$a=6$, $b=-5n$, $c=7$.
From the values of $a$, $b$, $c$, the value of $ab$ will be
$\begin{align}
  & \Rightarrow ab=6\left( -5n \right) \\
 & \Rightarrow ab=-30n \\
\end{align}$
Again, from the values of $a$, $b$, $c$, the value of $ac$ will be
$\begin{align}
  & \Rightarrow ac=6\left( 7 \right) \\
 & \Rightarrow ac=42 \\
\end{align}$
From the distribution law of multiplication, we can write the value of $a\left( b+c \right)$ as $ab+ac$. Mathematically we can write it as
$\Rightarrow a\left( b+c \right)=ab+ac$
Substituting the all the values we have in the above equation, then we will get
$\Rightarrow 6\left( -5n+7 \right)=-30n+42$

Hence the simplified form of the given value $6\left( -5n+7 \right)$ is $-30n+42$.

Note: We can also use another method to solve this problem. We can rearrange the terms in the given value as
$\Rightarrow 6\left( -5n+7 \right)=6\left( 7-5n \right)$
Now we can use the distribution law of multiplication over subtraction and simplify the equation to get the required result.