(2d%E2%88%922).jpeg "(−6d+6)(2d−2)")
Expanding the Expression (-6d + 6)(2d - 2)
This article will guide you through the steps of expanding the algebraic expression (-6d + 6)(2d - 2).
Understanding the Concept
Expanding an algebraic expression means multiplying out all the terms within parentheses. This involves applying the distributive property, which states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Step-by-Step Expansion
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Distribute the first term of the first parenthesis over the second parenthesis:
- (-6d)(2d - 2) + (6)(2d - 2)
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Apply the distributive property again to both terms:
- (-6d * 2d) + (-6d * -2) + (6 * 2d) + (6 * -2)
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Simplify each term by multiplying:
- -12d² + 12d + 12d - 12
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Combine like terms:
- -12d² + 24d - 12
The Final Answer
Therefore, the expanded form of (-6d + 6)(2d - 2) is -12d² + 24d - 12.
Key Points to Remember
- Always apply the distributive property carefully to ensure all terms are multiplied correctly.
- Combine like terms to simplify the expression as much as possible.
- Remember the rules of multiplication with signs (e.g., negative times negative equals positive).
This process of expanding algebraic expressions is a fundamental skill in algebra and is essential for solving equations, simplifying expressions, and performing various algebraic operations.