๐ Topic Summary
The distributive property is a fundamental concept in algebra that allows you to multiply a single term by two or more terms inside a set of parentheses. Think of it as 'distributing' the outside term to each term inside the parentheses. Once you've distributed, you can often simplify the expression by combining like terms. This worksheet will provide exercises to help you practice expanding expressions using the distributive property and then simplifying the result.
Expanding expressions using the distributive property involves multiplying each term inside the parentheses by the term outside. For example, $a(b + c)$ expands to $ab + ac$. Simplifying involves combining like terms after expanding. Like terms have the same variable raised to the same power (e.g., $3x$ and $5x$ are like terms, but $3x$ and $5x^2$ are not).
๐ง Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| Distributive Property |
a. Terms that have the same variable raised to the same power. |
| Expression |
b. A mathematical phrase containing numbers, variables, and operators. |
| Variable |
c. A property stating that $a(b + c) = ab + ac$. |
| Like Terms |
d. A symbol (usually a letter) representing a value that is not yet known. |
| Coefficient |
e. A number multiplied by a variable. |
โ๏ธ Part B: Fill in the Blanks
The ________ property states that you can multiply a single term by each term inside the ________. This is often used to ________ expressions, and then we can ________ like terms to simplify them. For example, in the expression $2(x + 3)$, we ________ the 2 to both $x$ and 3.
๐ค Part C: Critical Thinking
Explain in your own words why the distributive property is useful in simplifying algebraic expressions. Give an example of how it makes calculations easier.