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Expanding the Expression (5n-5)(2+2n)
This article will guide you through the process of expanding the algebraic expression (5n-5)(2+2n). We will use the distributive property to achieve this.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the results. In simpler terms: a(b + c) = ab + ac
Applying the Distributive Property
We can apply the distributive property twice to expand our expression:
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First Distribution:
- Treat (5n-5) as a single term and distribute it over the terms inside the second parenthesis (2+2n).
- This gives us: (5n-5) * 2 + (5n-5) * 2n
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Second Distribution:
- Now, distribute each term inside the first parenthesis (5n-5) to the terms outside.
- This gives us: 5n * 2 - 5 * 2 + 5n * 2n - 5 * 2n
Simplifying the Expression
Finally, we can simplify the expression by combining like terms:
- 10n - 10 + 10n² - 10n
- 10n² - 10
The Expanded Expression
Therefore, the expanded form of the expression (5n-5)(2+2n) is 10n² - 10.
Key Points to Remember
- The distributive property is a fundamental tool for simplifying algebraic expressions.
- Always remember to combine like terms after distributing.
By understanding and applying the distributive property, you can effectively expand and simplify algebraic expressions like (5n-5)(2+2n).