Question

) Which problem below would require that you use the distributive property to help yousimplify it? Explain why the distributive property is required for that problem. What wouldyou use to simplify the other problem?2 (x+4)5+ 9(5-1)

Answer 1

Given the expressions:

`\begin{gathered} 2(x+4) \\ 5+9\mleft(5-1\mright) \end{gathered}`

You need to remember that the Distributive Property states that:

`a(b\pm c)=ab\pm ac`

• In order to simplify the first expression, you only need to apply the Distributive Property, because there is a number multiplying a Sum. Therefore, get:

`\begin{gathered} =(2)(x)+(2)(4) \\ =2x+8 \end{gathered}`

• In order to simplify the second expression, you need to follow these steps:

1. Apply the Distributive Property:

`=5+(9)(5)-(9)(1)`

`=5+45-9`

2. Solve the Addition:

`=41`

Hence, the answers are:

• The first problem requires to use only the Distributive Property to simplify it. It is required because there is a number multiplying a Sum:

`2(x+4)`

Notice that the second expression can be simplified using the Distributive Property as the first step.

• The second problem can be simplified by applying the Distributive Property and then adding the numbers.