Find the H.C.F. of 3a2b and 4ab2 and factorize 3a2b + 4ab2.

The numerical factors of 3 are 1 and 3. The variable factors of $a^2$ are $a$ and $a^2$. The variable factors of $b$ is $b$. We combine these to find all possible factors.

$$3a^2b: 1, 3, a, a^2, b, 3a, 3a^2, 3b, ab, a^2b, 3ab, 3a^2b$$

The numerical factors of 4 are 1, 2, and 4. The variable factor of $a$ is $a$. The variable factors of $b^2$ are $b$ and $b^2$. We combine these to find all possible factors.

$$4ab^2: 1, 2, 4, a, b, b^2, 2a, 2b, 2b^2, 4a, 4b, 4b^2, ab, ab^2, 2ab, 2ab^2, 4ab, 4ab^2$$

(Highest Common Factor) of $3a^2b$ and $4ab^2$.
Find the HCF of the numerical coefficients and the HCF of the variable parts.
HCF of (3, 4) is 1.
HCF of ($a^2$, $a$) is $a$.
HCF of ($b$, $b^2$) is $b$.
Multiply these common factors together.

$$\text{H.C.F.} = 1 \cdot a \cdot b = ab$$

The H.C.F. of the algebraic expression is $\boxed{ab}$.

Factor out the H.C.F. ($ab$) from each term.

$$3a^2b + 4ab^2 = ab(3a + 4b)$$

The equivalent algebraic expression is $\boxed{ab(3a + 4b)}$.