SUMMARY
The 5th term of the expansion of $(2x+7)^8$ using the Binomial Theorem is $2689120x^4$. This result is derived from the formula for the binomial expansion, which states that the $m$th term is given by ${n \choose k}a^{n-k}b^k$. Specifically, for this case, the calculation involves ${8 \choose 4}(2x)^{4}(7)^4$, resulting in the final term of $2689120x^4$. Understanding the application of the Binomial Theorem is crucial for accurately determining specific terms in polynomial expansions.
PREREQUISITES
- Understanding of the Binomial Theorem
- Familiarity with binomial coefficients
- Basic algebraic manipulation skills
- Knowledge of polynomial expansion
NEXT STEPS
- Study the derivation of binomial coefficients using Pascal's Triangle
- Learn how to apply the Binomial Theorem to different polynomial expressions
- Explore advanced applications of the Binomial Theorem in combinatorics
- Practice calculating specific terms in polynomial expansions using various examples
USEFUL FOR
Students preparing for exams in algebra, educators teaching polynomial expansions, and anyone seeking to enhance their understanding of the Binomial Theorem and its applications in mathematics.
