Question

How do you simplify $ 4\left( 2x-3 \right) $ ?

Answer 1

Hint: In this problem we need to simplify $ 4\left( 2x-3 \right) $ . We can clearly observe that the given equation is an example for the distribution law of multiplication over subtraction. We have the distribution law of multiplication over subtraction as ‘If $ a $ , $ b $ , $ c $ are any variables and they are in the form of $ a\left( b-c \right) $ , then the value of the equation $ a\left( b-c \right) $ is given by distributing the variable $ a $ over the brackets mathematically we can write it as $ ab-ac $ ’. So finally, from the distribution law of multiplication over subtraction we have the formula $ a\left( b-c \right)=ab-ac $ . From this formula, we will calculate or simplify the given equation.

Complete step by step answer:
Given that $ 4\left( 2x-3 \right) $ .
Comparing the above given equation with $ a\left( b-c \right) $ , then we will get
 $ a=4 $ , $ b=2x $ , $ c=3 $
Now the value of $ ab $ is given by
 $ \begin{align}
  & ab=4\times 2x \\
 & \Rightarrow ab=8x....\left( \text{i} \right) \\
\end{align} $
Now the value of $ ac $ is given by
 $ \begin{align}
  & ac=4\times 3 \\
 & \Rightarrow ac=12...\left( \text{ii} \right) \\
\end{align} $
From the distribution law of multiplication over the subtraction we can write
 $ a\left( b-c \right)=ab-ac $
Substituting the all the values we have, $ a=4 $ , $ b=2x $ , $ c=3 $ and from equations $ \left( \text{i} \right) $ and $ \left( \text{ii} \right) $ we will get
$ \therefore 4\left( 2x-3 \right)=8x-12 $.

Note:
 We also have the distribution law of multiplication over the addition. This law states that ‘If $ a $ , $ b $ , $ c $ are any variables and they are in the form of $ a\left( b+c \right) $ , then the value of the equation $ a\left( b+c \right) $ is given by distributing the variable $ a $ over the brackets mathematically we can write it as $ ab+ac $ ’. If the problem is given like $ 4\left( 2x+3 \right) $ then we need to use the distribution law of multiplication over the addition which is given above.