Algebraic Expressions

24. An Algebraic Expression.

An algebraic expression is a number written with algebraic symbols. An algebraic expression may consist of one symbol, or of several symbols connected by signs.

Thus, $a$, $3abc$, $5a+2b-3c$, are algebraic expressions.

25. Terms.

A term is an algebraic expression, the parts of which are not separated by the sign $+$ or $-$.

Thus, $a$, $5xy$, $2ab\times 4cd$, ${\displaystyle \frac{3ab}{4cd}}$ are algebraic expressions of one term each. A term may be separated into parts by the sign $\times$ or $÷$.

26. Simple Expressions.

An algebraic expression of one term is called a simple expression or monomial.

Thus, $5xy$, $7a\times 2b$, $7a÷2b$, are simple expressions.

27. Compound Expressions.

An algebraic expression of two or more terms is called a compound expression or polynomial.

Thus, $5xy+7a$, $2x-y-3z$, $4a-3b+2c-3d$ are compound expressions.

A polynomial of two terms is called a binomial; of three terms, a trinomial.

Thus, $3a-b$ is a binomial; and $3a-b+c$ is a trinomial.

29. Positive and Negative Terms.

The terms of a compound expression preceded by the sign $+$ are called positive terms, and the terms preceded by the sign $-$ are called negative terms. The sign $+$ before the first term is omitted.

A positive and a negative term of the same numerical value cancel each other when combined.

31. Like Terms.

Terms which have the same combination of letters are called like or similar terms; terms which do not have the same combination of letters are called unlike or dissimilar terms.

Thus, $5a^{2}bc$, $-7a^{2}bc$, $a^{2}bc$, are like terms; but $5a^{2}bc$, $5a{b}^{2}c$, $5ab{c}^2$, are unlike terms.