91Ó°ÊÓ

In algebra, coefficients are the numerical parts of terms that include a variable. For example, in the term \(8c\), the coefficient is \(8\). Coefficients indicate how many times a variable is multiplied.

When multiplying algebraic expressions, start by multiplying the coefficients first. Identifying these coefficients makes the multiplication process clear and manageable.

For the exercise \((8c)(-2d)\), the coefficients are 8 and -2. By multiplying them together:

\(8 \times -2 = -16\).

This step simplifies the term to be multiplied with variables next.

Variables represent unknown values in algebraic expressions, commonly denoted by letters like \(a, b, x, y,\) or \(c\) and \(d\). In the multiplication \((8c)(-2d)\), the variables are \(c\) and \(d\).

When dealing with variables, multiply them just as you would numbers. However, if the variables are different, simply write them next to each other.

For instance, when multiplying \(c\) and \(d\) in the given exercise: \br>
\(c \times d = cd\).

This multiplication doesn't simplify further because \(c\) and \(d\) are distinct.

The Distributive Property is a fundamental concept in algebra used to simplify expressions and perform multiplication across terms within parentheses. It states that for any numbers or variables \(a, b,\) and \(c\), the expression \(a(b + c)\) is equal to \(ab + ac\).

In the given exercise, although not directly applied, understanding the distributive property can help in more complex problems.

For instance, suppose we have the expression \((3 + 4c)(2d)\). Using the distributive property:

\((3 + 4c)(2d) = 3(2d) + 4c(2d) = 6d + 8cd\).

Even though the original problem involves straightforward multiplication \((8c)(-2d)\), future problems might require you to distribute terms first and then simplify.