Simplifying the Expression (6a6)(2a^24a8)
This article will guide you through simplifying the expression (6a6)(2a^24a8) using the distributive property.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In simpler terms, it allows us to multiply a single term by each term within parentheses.
Example:
 a(b + c) = ab + ac
Applying the Distributive Property

Expand the first parenthesis: We begin by multiplying each term inside the second parenthesis by the first term of the first parenthesis (6a).
 (6a)(2a^24a8) = 12a^3  24a^2  48a

Expand the second parenthesis: Now, we multiply each term inside the second parenthesis by the second term of the first parenthesis (6).
 (6)(2a^24a8) = 12a^2 + 24a + 48

Combine like terms: We combine the terms we obtained in step 1 and step 2.
 12a^3  24a^2  48a + 12a^2 + 24a + 48

Simplify: Combining the terms with the same variable and exponents.
 12a^3  12a^2  24a + 48
Final Result
The simplified expression is 12a^3  12a^2  24a + 48.
This simplified expression represents the expanded form of the original expression. It can be used for further algebraic operations or to solve for specific values of 'a'.