Math Problem Statement
(a-2b)^3 answer first then soulution, then what method should I use? FOIL or box?
Solution
Answer:
The expression expands to .
Solution:
To expand , we can follow these steps:
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Start with the Binomial Theorem: The Binomial Theorem states that can be expanded as: Here, , , and .
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Apply the Binomial Expansion: Expand using the binomial coefficients: Simplifying each term:
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Combine the terms: Putting it all together gives:
Method: FOIL or Box?
For this specific problem:
- Neither FOIL nor the box method is typically used directly to expand a binomial raised to a power greater than 2.
- Binomial expansion is more appropriate.
However, if you are expanding a cubic binomial like this by multiplying step-by-step, then Box method (also known as area method) can be useful for organizing the multiplication in stages. For example, first multiply by , then multiply the result by again.
Would you like more details on any of these steps or have any questions?
Follow-Up Questions:
- How would you expand using the Binomial Theorem?
- Can you use the Box method to expand ?
- What are the advantages of using the Binomial Theorem over FOIL for higher powers?
- How does the sign of the middle terms change when expanding compared to ?
- What is the difference between the Binomial Theorem and Pascal's Triangle in expansion?
Tip:
When expanding binomials, remember that the Binomial Theorem works efficiently for any power, especially when the exponent is greater than 2.
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Math Problem Analysis
Mathematical Concepts
Binomial Theorem
Binomial Expansion
Formulas
Binomial Theorem: (x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k
Theorems
Binomial Theorem
Suitable Grade Level
High School