%5E3.jpeg "(9c-1)^3")
Expanding (9c - 1)³
This article explores the expansion of the expression (9c - 1)³.
Understanding the Problem
The expression (9c - 1)³ represents the product of (9c - 1) multiplied by itself three times:
(9c - 1)³ = (9c - 1) * (9c - 1) * (9c - 1)
Expanding the Expression
To expand this expression, we can use the distributive property and FOIL method:
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Expand the first two terms: (9c - 1) * (9c - 1) = 81c² - 9c - 9c + 1 = 81c² - 18c + 1
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Multiply the result by the third term: (81c² - 18c + 1) * (9c - 1) = 729c³ - 162c² + 9c - 81c² + 18c - 1
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Combine like terms: 729c³ - 243c² + 27c - 1
Final Result
Therefore, the expanded form of (9c - 1)³ is 729c³ - 243c² + 27c - 1.
Key Points
- Distributive property: This property allows us to multiply each term within a set of parentheses by a factor outside of the parentheses.
- FOIL method: This acronym stands for "First, Outer, Inner, Last" and helps us multiply two binomials by systematically multiplying each term of the first binomial by each term of the second binomial.