Factor the expression xy + 5y + 2x + 10 by grouping.

The algebraic expression is $xy + 5y + 2x + 10$.

Observe the four terms: $xy$, $5y$, $2x$, 10.
There is no common factor (other than 1) that divides all four terms.

• 2.1 There is no common factor for all four terms.

Consider the two groups: Group 1 is $(xy + 5y)$ and Group 2 is $(2x + 10)$.
In Group 1, $y$ is a common factor.
In Group 2, 2 is a common factor.

• 2.2 Each group has a common factor.

Factor out the common value from each group.
For Group 1: $xy + 5y = y(x + 5)$
For Group 2: $2x + 10 = 2(x + 5)$
Combine the factored groups to write the equivalent algebraic expression.

• 2.3 The equivalent algebraic expression is $\boxed{y(x + 5) + 2(x + 5)}$

Identify the common factor in the two terms obtained in Step 4: $y(x + 5)$ and $2(x + 5)$.
The common factor is $(x + 5)$.

• 2.4 The common factor in the two terms is $\boxed{(x + 5)}$