(2%2B2n).jpeg "(5n−5)(2+2n)")
Expanding the Expression (5n−5)(2+2n)
This article explores the expansion of the expression (5n−5)(2+2n). We will achieve this through the use of the distributive property.
The Distributive Property
The distributive property states that for any numbers a, b, and c, the following equation holds true:
a(b + c) = ab + ac
This property allows us to multiply a sum by a single term by distributing the multiplication over each term in the sum.
Expanding the Expression
Let's apply the distributive property to our expression:
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Distribute the 5n: (5n−5)(2+2n) = 5n(2+2n) - 5(2+2n)
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Distribute the -5: 5n(2+2n) - 5(2+2n) = 10n + 10n² - 10 - 10n
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Combine like terms: 10n + 10n² - 10 - 10n = 10n² - 10
Conclusion
Therefore, the expanded form of the expression (5n−5)(2+2n) is 10n² - 10. This process showcases the power of the distributive property in simplifying expressions and making them easier to work with.