Question

Which of the following is a simplified version of 122(x+1) 5?

Answer 1

To simplify the expression \(122(x+1)^5\), we can use the binomial expansion formula. However, since you're looking for a simplified version, it is sufficient to express it in a more manageable form without fully expanding it.

1. **Leave it in factored form**:
\[
122(x+1)^5
\]
This is already a simplified version, as it clearly shows the coefficient and the factored expression.

2. **If you're looking for a binomial expansion**:
Using the binomial theorem for expansion:
\[
(x + 1)^5 = \sum_{k=0}^{5} \binom{5}{k} x^k 1^{5-k} = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1
\]
Therefore,
\[
122(x + 1)^5 = 122(x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1)
\]
Expanding this out gives:
\[
122x^5 + 610x^4 + 1220x^3 + 1220x^2 + 610x + 122
\]

In summary, the expression can be left as \(122(x+1)^5\) for a compact form, or expanded fully to find each individual term contributed to the polynomial. If you need something specific, please clarify!