Determine the H.C.F. of 3a²b + 4ab²?

The H.C.F. (Highest Common Factor) of 3a²b and 4ab² can be found by factoring each term and identifying the common factors.

3a²b = 3 * a * a * b
4ab² = 2 * 2 * a * b * b

The common factors between 3a²b and 4ab² are 1, a, and b. Therefore, the H.C.F. of 3a²b and 4ab² is a * b = ab.

Step 1: Find the factors of each term.

- 3a²b = 3 × a × a × b
- 4ab² = 4 × a × b × b

Step 2: Identify the common factors.

The common factors are a and b.

Step 3: Multiply the common factors.

H.C.F. = a × b

Therefore, the H.C.F. of 3a²b and 4ab² is ab.