Question

Expand Using the Binomial Theorem (s+4v)^5

Answer 1

To expand (s+4v)^5 using the Binomial Theorem, each term is constructed from the coefficients of Pascal's Triangle, with the powers of s decreasing and the powers of 4v increasing in each term.

Step-by-step explanation:

The question requires us to expand (s+4v)^5 using the Binomial Theorem. The Binomial Theorem expresses the expansion of the power of a binomial as a sum. For the expansion of (a + b)^n, it's given by the formula a^n + n * a^(n-1) * b + n * (n-1)/2 * a^(n-2) * b^2 + ... + b^n. Applying this to our expression, we get:

1. s^5
2. + 5 * s^4 * 4v
3. + 10 * s^3 * (4v)^2
4. + 10 * s^2 * (4v)^3
5. + 5 * s * (4v)^4
6. + (4v)^5

Each term is based on the coefficients from Pascal's Triangle and the powers of s and 4v decrease and increase respectively in each successive term.