Math Problem Statement
Expand the given binomial: (4x - 3y)^5
Solution
The binomial in your image is . To expand this, we will use the binomial theorem, which states:
Here:
- ,
- ,
- .
The expansion will involve the binomial coefficients for , where each term follows the pattern:
Let's calculate the terms one by one:
- For :
- For :
- For :
- For :
- For :
- For :
So, the expanded form is:
Would you like further explanation on any step?
Here are some related questions to expand on this:
- How does the binomial theorem apply to higher powers?
- How do binomial coefficients relate to Pascal's Triangle?
- What is the general form of a binomial expansion?
- How does expanding a binomial differ for positive and negative terms?
- What are some real-world applications of the binomial expansion?
Tip: When expanding binomials, ensure the correct application of negative signs to avoid errors, especially when powers of negative numbers are involved.
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Math Problem Analysis
Mathematical Concepts
Algebra
Binomial Theorem
Polynomials
Formulas
(a + b)^n = sum_{k=0}^{n} binom(n,k) a^{n-k} b^k
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12