x6-distributive-property.jpeg "(7-4n)x6 Distributive Property")
Using the Distributive Property with (7 - 4n) x 6
The distributive property is a fundamental concept in algebra that allows us to simplify expressions involving multiplication. It states that multiplying a sum by a number is the same as multiplying each term of the sum by that number individually.
In this case, we have (7 - 4n) multiplied by 6. To apply the distributive property, we need to distribute the 6 to each term inside the parentheses:
(7 - 4n) x 6 = 7 x 6 - 4n x 6
Now, we can simplify the multiplication:
42 - 24n
Therefore, the expression (7 - 4n) x 6, when simplified using the distributive property, is equal to 42 - 24n.
Key Points to Remember:
- Distributive Property: a(b + c) = ab + ac
- Multiplication over Subtraction: The distributive property works with both addition and subtraction.
- Order of Operations: Remember to multiply before combining like terms.
Example:
Let's say n = 2. We can substitute this value into our simplified expression:
42 - 24n = 42 - 24(2) = 42 - 48 = -6
Therefore, if n = 2, then (7 - 4n) x 6 = -6.
Conclusion
Understanding the distributive property is crucial for simplifying algebraic expressions. By applying this property correctly, we can break down complex expressions into simpler terms and solve for variables efficiently.