Question

Which expression is equivalent to 5b + 7 - 9b + 35b - 7 - 9b³?

1) 5b + 7 - 9b + 35b - 7 - 9b³
2) 5b + 7 - 9b + 35b - 7 - 9b²
3) 5b + 7 - 9b + 35b - 7 - 9b⁴
4) 5b + 7 - 9b + 35b - 7 - 9b⁵

Answer 1

The expression equivalent to
`\(5b + 7 - 9b + 35b - 7 - 9b³\) is option 1) \(5b + 7 - 9b + 35b - 7 - 9b³\).`

Step-by-step explanation:

The given expression is a combination of terms involving the variable
`\(b\). To simplify, we can combine like terms by grouping the \(b\)` terms together. The simplified expression becomes
`\(5b - 9b + 35b - 9b³ + 7 - 7\).` Now, combining the
`\(b\) terms, we get \(26b - 9b³\)`. The final answer corresponds to option 1)
`\(5b + 7 - 9b + 35b - 7 - 9b³\)`, as it correctly represents the simplified form
`\(26b - 9b³\).`

In option 2),
`\(9b²\)` is present, which is not part of the simplified expression. Options 3) and 4) include terms with powers of
`\(b\)` that are not present in the original expression. Therefore, option 1) is the accurate representation of the given expression after simplification.