(-2a%5E2-4a-8).jpeg "(6a-6)(-2a^2-4a-8)")
Simplifying the Expression (6a-6)(-2a^2-4a-8)
This article will guide you through simplifying the expression (6a-6)(-2a^2-4a-8) 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
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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^2-4a-8) = -12a^3 - 24a^2 - 48a
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Expand the second parenthesis: Now, we multiply each term inside the second parenthesis by the second term of the first parenthesis (-6).
- (-6)(-2a^2-4a-8) = 12a^2 + 24a + 48
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Combine like terms: We combine the terms we obtained in step 1 and step 2.
- -12a^3 - 24a^2 - 48a + 12a^2 + 24a + 48
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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'.