Algebra 1 Distributive Property Worksheet
The distributive property is a fundamental concept in algebra that helps us expand and simplify expressions. It states that for any real numbers a, b, and c:
a(b + c) = ab + ac
In this worksheet, we will practice applying the distributive property to simplify various expressions.
Section 1: Simple Expressions
Simplify the following expressions using the distributive property:
- 2(x + 3) =
- 5(y - 2) =
- 3(2x + 1) =
- 4(3y - 2) =
- x(2 + 3) =
📝 Note: Remember to multiply the outside number with each term inside the parentheses.
Section 2: Multi-Term Expressions
Simplify the following expressions using the distributive property:
- 2(x + 3y) =
- 3(2x - 4y) =
- 4(x + 2y - 3) =
- 5(2x - y + 1) =
- x(3y + 2z) =
📝 Note: Be careful when dealing with multiple terms inside the parentheses. Make sure to multiply the outside number with each term.
Section 3: Word Problems
Read each problem carefully and use the distributive property to solve:
- Tom has 2 groups of 3 pencils and 2 groups of 4 pens. How many writing instruments does Tom have in total?
- A bookshelf has 5 shelves, and each shelf can hold 2 rows of 3 books. How many books can the bookshelf hold in total?
- A bakery sells 2 types of bread: whole wheat and white. They sell 3 whole wheat loaves and 2 white loaves per hour. If they operate for 4 hours, how many loaves of bread do they sell in total?
Section 4: Challenge Problems
Simplify the following expressions using the distributive property:
- 2(x + 3y - 2z) =
- 3(2x - 4y + 5z) =
- 4(x + 2y - 3z + 1) =
- 5(2x - y + 2z - 3) =
- x(3y + 2z - 4w) =
📝 Note: These problems require more advanced application of the distributive property. Take your time and work carefully.
What is the distributive property in algebra?
+The distributive property is a mathematical concept that states a single operation (like multiplication) can be applied to multiple values (like addition or subtraction) simultaneously.
Why is the distributive property important in algebra?
+The distributive property is crucial in algebra as it helps simplify complex expressions, making it easier to solve equations and manipulate formulas.
How do I apply the distributive property to expressions with multiple terms?
+When dealing with expressions containing multiple terms, multiply the outside number with each term inside the parentheses, being careful to keep track of each term's sign.
In conclusion, mastering the distributive property is essential for success in algebra and beyond. By practicing the exercises and problems in this worksheet, you will become more confident and proficient in applying this fundamental concept to a wide range of mathematical expressions and problems.
Related Terms:
- Easy Distributive Property Worksheet PDF
