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Technical Mathematics, Sixth Edition by Michael A. Calter Ph.D., Paul A. Calter

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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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