Final answer:
The expression vw - 5v - 7w + 35 can be factored by grouping similar terms and factoring out the common factors to obtain v(w - 5) - 7(w - 5), which is option a.
Step-by-step explanation:
To factor by grouping the expression vw - 5v - 7w + 35, we need to group terms that have common factors and then factor out those common factors.
First, we group the terms with a common 'v' and those with a common 'w':
(vw - 5v) - (7w - 35)
Next, we factor out the common factors in each group:
v(w - 5) - 7(w - 5)
Now, we can see that the expression (w - 5) is common in both terms, so we can factor that out as well:
(w - 5)(v - 7)
The correct factored form of the expression is therefore v(w - 5) - 7(w - 5), which corresponds to option a in the list provided by the student.