Explain factoring by grouping and factoring out the highest common factor with examples.

To find an equivalent expression by factoring, like with $3a^2b + 4ab^2$:

For expressions suitable for factoring by grouping, there is usually no common factor shared by all four terms.

Each group (e.g., the first two terms and the last two terms) has its own common factor.

Since the specific expression for Activity 2 is not provided, let's use a common example for factoring by grouping: $x^3 + 2x^2 + 3x + 6$.
Group 1: $x^3 + 2x^2$. The common factor is $x^2$. Factoring it out gives $x^2(x + 2)$.
Group 2: $3x + 6$. The common factor is 3. Factoring it out gives $3(x + 2)$.
The equivalent algebraic expression after factoring out common values from each group is:

From the expression $x^2(x + 2) + 3(x + 2)$, the common factor is the binomial term $\boxed{(x + 2)}$.