Final answer:
An unsimplified expression that simplifies to 20x+10 using the distributive property and combining like terms is 5(4x+2) + (5x + 5) - (5x + 5). When distributed and simplified, this expression becomes 20x+10.
Step-by-step explanation:
To create an unsimplified expression that uses the distributive property and requires combining like terms to simplify to 20x+10, let's start with the simplified expression and work backward.
We can break down 20x+10 into two expressions that will be combined: 5(4x+2) and 5x+5. When you distribute the 5 into the first expression, 5(4x+2), and combine it with the second expression, 5x+5, you will have 20x+10+5x+5. Now let's add another term that would cancel out when combining like terms. Include -5x in the expression. So the unsimplified expression can be written as:
5(4x+2) + 5x + 5 - 5x
When you apply the distributive property, you get 20x + 10 + 5x + 5 - 5x. Combining like terms: 20x + 5x - 5x + 10 + 5 simplifies to 20x + 15, but we want 20x + 10, so we adjust the constants:
5(4x+2) + (5x + 5) - (5x + 5)
Using distributive property and combining like terms, simplifies to:
20x + 10 + 5x + 5 - 5x - 5 = 20x + 10