Math Problem Statement
Find the 4th term in the expansion of (a+b)^3 In simplest form
Solution
The expression given is , and we need to find the 4th term in its expansion.
The binomial expansion of is given by:
For , the expansion will be:
Simplifying, we get:
So, the terms of the expansion are:
Therefore, the 4th term in the expansion is .
Would you like details on binomial coefficients, or have any questions?
Here are 5 related questions:
- What is the 3rd term in the expansion of ?
- How do you calculate the binomial coefficient ?
- What is the general term formula in the binomial expansion of ?
- How can the binomial theorem be applied to solve problems in probability?
- How would the expansion differ if the expression were ?
Tip: In binomial expansions, each term is structured as a product of a binomial coefficient, one variable raised to a power, and the other variable raised to the complementary power.
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Math Problem Analysis
Mathematical Concepts
Binomial Theorem
Binomial Coefficients
Formulas
Binomial expansion formula (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
Theorems
Binomial Theorem
Suitable Grade Level
High School