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rated from each other by the signs $+$ and $-$. Thus, $7a+5b-3c-x+2y$ is an expression consisting of five terms.

Note. When no sign precedes a term the sign $+$ is understood.

3. Expressions are either simple or compound. A simple expression consists of one term, as $5a$. A compound expression consists of two or more terms. Compound expressions may be further distinguished. Thus an expression of two terms, as $3a-2b$, is often called a binomial, and one of three terms, as $2a+3b+c$, a trinomial. Simple expressions are frequently spoken of as monomials, and compound expressions as multinomials or polynomials.

4. When two or more quantities are multiplied together the result is called the product. One important difference between the notation of Arithmetic and Algebra should be here remarked. In Arithmetic the product of $2$ and $3$ is written $2\times 3$, whereas in Algebra the product of $a$ and $b$ may be written in any of the forms $a\times b$, $a\cdot b$, or $ab$. The form $ab$ is the most usual. Thus, if $a=2$, $b=3$, the product $ab=a\times b=2\times 3=6$; but in Arithmetic $23$ means "twenty-three," or $2\times 10+3$.

5. Each of the quantities multiplied together to form a product is called a factor of the product. Thus $5$, $a$, $b$ are the factors of the product $5ab$.

Note. The beginner should carefully notice the difference between term and factor.

6. When one of the factors of an expression is a numerical quantity, it is called the coefficient of the remaining factors. Thus, in the expression $5ab$, $5$ is the coefficient. But the word coefficient is also used in a wider sense, and it is sometimes convenient to consider any factor, or factors, of a product as the coefficient of the remaining factors. Thus, in the product $6abc$, $6a$ may be appropriately called