Question

Explain how you can use the distributive property to simplify the expression 5(2x+3).

Answer 1

The distributive property is very useful for simplifying expressions. Let's break down how you can use it to simplify the expression
`5(2x+3)`.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In algebraic terms, this is written as
`a(b+c)=ab+ac`.

Applying the Distributive Property to 5(2x+3)

Now, let's apply this property to your expression:

1. Expression:
`5(2x+3)`

Here,
`a=5`,
`b=2x`, and
`c=3`.

2. Distribute 5 to Each Term in the Parentheses:

• Multiply
  `5` with
  `2x`:
  `5`×
  `2x=10x`
• Multiply
  `5` with
  `3`:
  `5`×
  `3=15`

3. Combine the Products:

After distributing, you combine these products:
`10x+15`.

Simplified Expression

So,
`5(2x+3)` simplifies to
`10x+15`