Question

How do you use the distributive property to simplify $ 5\left( 3x-2 \right) $ ?

Answer 1

Hint:
We start solving the problem by recalling the distributive property as the multiplication distributes over the addition and then the representation of the property as $ a\left( b\pm c \right)=ab\pm ac $ . We then consider the suitable values for a, b and c to apply the distributive property. We then recall the associative property of multiplication as $ a\left( bc \right)=\left( ab \right)c $ and apply it in the result obtained after applying the distributive property. We then make the necessary calculations to get the required answer.

Complete step by step answer:
According to the problem, we are asked to find the value of $ 5\left( 3x-2 \right) $ using the distributive property.
Let us first recall the definition of the distributive property.
We know that the distributive property is defined as the multiplication distributes over the addition, which is represented as follows: $ a\left( b\pm c \right)=ab\pm ac $ .
So, we have $ 5\left( 3x-2 \right) $ . Let us assume $ a=5 $ , $ b=3x $ and $ c=2 $ .
So, we get $ 5\left( 3x-2 \right)=5\left( 3x \right)-5\left( 2 \right) $ ---(1).
From associative property of multiplication, we know that $ a\left( bc \right)=\left( ab \right)c $ . Let us use this result in equation (1).
 $ \Rightarrow 5\left( 3x-2 \right)=\left( 5\times 3 \right)x-10 $ .
 $ \Rightarrow 5\left( 3x-2 \right)=15x-10 $ .
So, we have found the value of $ 5\left( 3x-2 \right) $ as $ 15x-10 $ .
 $ \therefore $ The value of $ 5\left( 3x-2 \right) $ is $ 15x-10 $ .

Note:
 Whenever we get this type of problem, we first try to recall the definitions that were helpful to solve the equations given in the problem. We should not confuse while assuming the values of a, b, and c as this will change the obtained answer a lot. We can expect problems that can be solved by making use of the distributive property \[\left( a\pm b \right)c=ac\pm bc\].