Find the H.C.F. of the algebraic expression 3a2b + 4ab2 and express it in factored form.

The two terms are $3a^2b$ and $4ab^2$.
For the term $3a^2b$:

$$3a^2b = 3 \times a \times a \times b$$

The individual factors are 3, $a$, $a$, $b$.

For the term $4ab^2$:

$$4ab^2 = 2 \times 2 \times a \times b \times b$$

The individual factors are 2, 2, $a$, $b$, $b$.

(Highest Common Factor) of the algebraic expression $3a^2b + 4ab^2$.
To find the H.C.F., we look for common factors in both terms.
Factors of $3a^2b$: $3, a, a, b$
Factors of $4ab^2$: $2, 2, a, b, b$

The common factors are $a$ and $b$.
The numerical coefficients are 3 and 4. Their H.C.F. is 1.
Therefore, the H.C.F. of $3a^2b$ and $4ab^2$ is $a \times b = ab$.

The H.C.F. found in Step 2 is $ab$.
Factor $ab$ from each term:

$$3a^2b + 4ab^2 = ab \left( \frac{3a^2b}{ab} + \frac{4ab^2}{ab} \right)$$ $$3a^2b + 4ab^2 = ab(3a + 4b)$$

a) The possible factors for $3a^2b$ are: $\boxed{\text{3, a, a, b}}$
The possible factors for $4ab^2$ are: $\boxed{\text{2, 2, a, b, b}}$

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

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