What is 6(-5n + 7) simplified?
The Correct Answer and Explanation is:
The expression ( 6(-5n + 7) ) can be simplified by distributing the 6 across the terms inside the parentheses. Here’s how you can do it step by step:
Step 1: Understand Distribution
The distributive property states that when you multiply a number by a sum or difference inside parentheses, you must multiply the number by each term inside the parentheses. In this case, you are multiplying 6 by both terms (-5n) and (+7).
Step 2: Apply the Distributive Property
Distribute the 6 to each term inside the parentheses:
[
6(-5n) + 6(7)
]
Step 3: Simplify Each Term
Now, simplify each term:
- (6(-5n)) becomes (-30n), because (6 \times -5 = -30).
- (6(7)) becomes (42), because (6 \times 7 = 42).
Step 4: Write the Final Simplified Expression
After distributing and simplifying, the expression becomes:
[
-30n + 42
]
Final Answer:
The simplified expression is (-30n + 42).
Explanation
The process of simplification uses the distributive property, which is a basic principle in algebra. It ensures that each term inside the parentheses is multiplied by the factor outside the parentheses. In this case, the factor is 6. By applying the distributive property, you avoid performing any unnecessary calculations later and can simplify expressions that involve variables and constants. This technique is essential for solving equations, simplifying algebraic expressions, and preparing for more complex algebraic manipulations. Understanding how to distribute and simplify is foundational to working with polynomials and linear expressions in algebra.