Final answer:
The next correct step in simplifying the algebraic expression –8k2 + k + 3k2 is to combine like terms, resulting in –5k2 + k.
Step-by-step explanation:
To simplify the expression –8k2 + k + 3k2, you need to combine like terms.
The like terms in this case are the terms that have the same variable to the same power, which are –8k2 and 3k2.
When we add these terms together, we combine their coefficients (the numbers in front of the variables) to get –(8–3)k2 which simplifies to –5k2.
The term k, being a different power of k, cannot be combined with the k2 terms, so we simply bring it down unchanged.
Thus, the next correct step in simplifying the expression is:–5k2 + k
Always remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.