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In mathematics, the distributive property is fundamental when working with expressions. This property allows you to multiply a single term by multiple terms inside a set of parentheses. Essentially, you are 'distributing' the multiplication over addition or subtraction. For instance, consider the expression:

• \(4a^{3}(3b^{2})\)

Using the distributive property, start by multiplying the constants (4 and 3) together, which focuses purely on their numerical values. Then, proceed to address the variables separately.
This method simplifies more extensive and complex expressions and ensures that every term inside the parentheses is correctly multiplied by the term outside.

Multiplying constants is a straightforward process in algebra. A constant is simply a number without any variable attached. When you multiply constants, you are performing basic arithmetic. For example, in the expression:

• \(4 \times 3\)

You multiply 4 and 3 to get 12. This multiplication step is essential before you proceed with combining any variables in the expression.
In the given exercise \(4a^{3}(3b^{2})\), after distributing, you multiply the constants 4 and 3 together to get 12. This process simplifies subsequent steps since you've dealt separately with numeric values first.
Remember, multiplying constants involves simple multiplication and serves as the foundation before moving on to the variable part of the product.

Combining variables is about simplifying terms involving variables once you have dealt with the constants. In algebraic expressions, variables represent unknown values and are often raised to powers. Combining variables means ensuring that each variable's exponent is correctly represented.
In the expression \(a^{3} \times b^{2}\), since there are no like terms to combine, merely place the variables next to each other after handling the constants.

• \(a^{3} \times b^{2}\) becomes \(a^{3}b^{2}\)

Thus, after multiplying the constants and addressing the variables separately, you write the expression as:

• \(12a^{3}b^{2}\)

This final form represents the simplified product of the given terms.