Algebraic Expressions:

Unlike equations, algebraic expressions do not contain an equal sign.

 The word "terms" refers to values that are added or subtracted. 7n + 2 has two terms. The word "factors" refers to values that are multiplied. The term 7n has two factors: 7 and n.

The skill of translating between verbal statements and algebraic expressions requires an understanding of the words that are commonly used to represent mathematical operations.

A sampling of words used to represent mathematical operations:
 ADD SUBTRACT MULTIPLY DIVIDE add sum increased by more than exceeds total plus in all gain deposit subtract difference decreased by fewer less than * diminished by minus take away withdraw reduced by multiply product of times double triple twice divide quotient per divided equally split into fraction ratio of
* Remember that "less than" reverses the order of what you read. [ 6 less than x, becomes x - 6 ]

 Always look for the placement of commas in the verbal statements. They will help you decide how to properly group terms in your algebraic expression. For example:  the verbal statement "5 times, a number increased by 6" translates to 5(n + 6) and is not 5n + 6.

 (Remember that variables can be represented by any letter or symbol, unless otherwise directed.)
 Verbal Statement Algebraic Expression 1. Five increased by four times a number 5 + 4n 2. Eight less than twice a number 2n - 8 3. Three times a number, increased by 9 3n + 9 4. The product of 4, and a number decreased by 7 4(n - 7) 5. The number of feet in x yards. 3x 6. Express the width of a rectangle which is seven less than its length, l. l - 7 7. A number repeated as a factor 3 times. n • n • n = n3

Terms used to refer to specific expressions:

 TERM DESCRIPTION EXAMPLES monomial The product of non-negative integer powers of variables. It has ONE term. (mono implies one) 12, -3x, 2x2, -7ab, 4t3s4 binomial The sum of two monomials. It has TWO unlike terms. (bi implies two) 7x + 4,  x2 +1,  3a - 2b trinomial The sum of three monomials. It has THREE unllike terms. (tri implies three) x2 + 4x + 4,  4p2 - 3q3 - 1 polynomial A generic term for the sum of one or more monomials. (poly implies many) 4x,  s + 2,  a2 + b2 + c

Algebraic Equations:

Unlike expressions, algebraic equations contain an equal sign.
EQUA
tion EQUAl sign

You will still encounter the "words" used to represent mathematical operations, as shown in the chart at the top of the page. To that list, we can now add a sampling of words that imply "an equal sign".

 EQUAL is, are, was, were, equivalent to, same as, yields, gives