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### 2.4. Multiplying a Monomial by a Monomial

From addition and subtraction of algebraic expressions we now move on to multiplication. We will start with the simplest types and then progress to the more complex.

#### 2.4.1. Symbols and Definitions

Multiplication is indicated in several ways: by the usual × symbol; by a dot; or by parentheses, brackets, or braces. Thus the product of b and d could be written

b · d b × d b(d) (b)d (b)(d)

We learned earlier that the symbols of grouping (parentheses, brackets, and braces) indicate that the enclosed terms are to be taken as a whole. Here we see that they also indicate multiplication.

## Example 46:

1. m(n) means the product of m and n.

2. −3x(2y) means the product of −3x and 2y.

Most common of all is to use no symbol at all. The product of b and d would usually be written bd. Avoid using the × symbol when doing algebra because it could get confused with the letter x.

We get a product when we multiply two or more factors.

(factor)(factor)(factor) = product

#### 2.4.2. Rules of Signs

When we multiply two factors that have the same sign, we get a product that is positive. When we multiply two factors that have opposite signs, we get a product that is negative. Stated as a rule, if a and b are positive quantities, we have

NOTE

The product of two factors of like signs is positive, of unlike signs is negative.

## Example 47:

The rules of signs are shown in these ...

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