Using the Distributive Property to Simplify Expressions
Apply the distributive property to simplify multi-term algebraic expressions in Grade 9 Algebra. Multiply through parentheses and combine like terms step by step.
Key Concepts
New Concept The Distributive Property lets you multiply a single value across terms inside parentheses, a key move for simplifying algebraic expressions.
The Distributive Property For all real numbers $a, b, c$, $$a(b + c) = ab + ac \quad \text{and} \quad a(b c) = ab ac$$ What’s next Now, let's put it into practice. You'll work through examples with different number types and variables before applying it to a real world problem.
Common Questions
What is the distributive property in algebra?
The distributive property states that a(b + c) = ab + ac. You multiply the term outside the parentheses by every term inside, then combine like terms. It is one of the most fundamental tools for simplifying expressions.
How do you use the distributive property to simplify expressions with multiple terms?
Multiply the factor outside the parentheses by each term inside individually. Then look for like terms—terms with the same variable and exponent—and add or subtract their coefficients to reach the simplest form.
What is a common mistake when using the distributive property?
Students often multiply only the first term inside the parentheses and forget the rest. Remember that every term inside must be multiplied by the outside factor, especially when subtraction is involved, since the sign must be distributed too.