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:

Expand the first two terms: (9c  1) * (9c  1) = 81c²  9c  9c + 1 = 81c²  18c + 1

Multiply the result by the third term: (81c²  18c + 1) * (9c  1) = 729c³  162c² + 9c  81c² + 18c  1

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.