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 What is an algebraic expression?

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PostSubject: What is an algebraic expression?   Wed Sep 24, 2008 7:47 am

ALGEBRAIC EXPRESSIONS
An algebraic expression is made up of the
signs and symbols of algebra. These symbols

include the Arabic numerals, literal numbers,

the signs of operation, and so forth. Such an

expression represents one number or one quantity. Thus, just as the sum of 4 and 2 is one


quantity, that is, 6, the sum of c and d is one

quantity, that is, c + d. Likewise , ab,
a - b, and so forth, are algebraic expressions each of which represents one quantity or


number.

Longer expressions may be formed by combinations of the various signs of operation and

the other algebraic symbols, but no matter how

complex such expressions are they still represent one number. Thus the algebraic expression
is one number

The arithmetic value of any algebraic expression depends on the values assigned to the

literal numbers. For example, in the expression 2x2 - 3ay, if x = -3, a = 5, and y = 1, then


we have the following:

2x2 - 3ay = 2(-3)2 -3(5)(1)



= 2(9) - 15 = 18 - 15 = 3

Notice that the exponent is an expression
such as 2x2 applies only to the x. If it is desired to indicate the square of 2x, rather than


2 times the square of x, then parentheses are

used and the expression becomes (2x)2.

Practice problems. Evaluate the following
algebraic expressions when a = 4, b = 2, c = 3,

x = 7, and y = 5. Remember, the order of operation is multiplication, division, addition, and


subtraction.


Answers:
1. 53

2. -29

3. 19

4. 53


TERMS AND COEFFICIENTS
The terms of an algebraic expression are
the parts of the expression that are connected

by plus and minus signs. In the expression

3abx + cy - k, for example, 3abx, cy, and k are

the terms of the expression.

An expression containing only one term, such
as 3ab, is called a monomial (mono means one).

A binomial contains two terms; for example,

2r + by. A trinomial consists of three terms.

Any expression containing two or more terms

may also be called by the general name, polynomial (poly means many). Usually special


names are not given to polynomials of more than

three times. The expression x3 - 3x2 + 7x + 1

is a polynomial of four terms. The trinomial

x2 + 2x + 1 is an example of a polynomial which

has a special name.

Practice problems. Identify each of the following expressions as a monomial, binomial,

trinomial, or polynomial. (Some expressions

may have two names.)


Answers:
1. Monomial

2. Trinomial (also polynomial)

3. Monomial

4. Polynomial

5. Binomial (also polynomial)

6. Binomial (also polynomial)

In general, a COEFFICIENT of a term is

any factor or group of factors of a term by

which the remainder of the term is to be multiplied. Thus in the term 2axy, 2ax is the coefficient of y, 2a is the coefficient of xy,
and 2 is

the coefficient of axy. The word "coefficient"

is usually used in reference to that factor which

is expressed in Arabic numerals. This factor
is sometimes called the NUMERICAL COEFFICIENT. The numerical coefficient is customarily written as the first factor of the term.

In 4x, 4 is the numerical coefficient, or simply

the coefficient, of x. Likewise, in 24xy2, 24 is

the coefficient of xy2 and in 16(a + b), 16 is the

coefficient of (a + b). When no numerical coefficient is written it is understood to be 1. Thus


in the term xy, the coefficient is 1.

COMBINING TERMS
When arithmetic numbers are connected by
plus and minus signs, they can always be combined into one number. Thus,


Here three numbers are added algebraically
(with due regard for sign) to give one number.

The terms have been combined into one term.

Terms containing literal numbers can be

combined only if their literal parts are the

same. Terms containing literal factors in

which the same letters are raised to the same

power are called like terms. For example, 3y

and 2y are like terms since the literal parts

are the same. Like terms are added by adding

the coefficients of the like parts. Thus, 3y + 2y

= 5y just as 3 bolts + 2 bolts = 5 bolts. Also


3a2b and a2b are like; 3a2b + a2b =
4a2b and

3a2b - a2b = 2a2b. The numbers ay and by
are

like terms with respect to y. Their sum could

be indicated in two ways: ay + by or (a +
b)y .

The latter may be explained by comparing the

terms to denominate numbers. For instance,

a bolts + b bolts = (a + b) bolts.

Like terms are added or subtracted by adding or subtracting the numerical coefficients

and placing the result in front of the literal

factor, as in the following examples:

7x2 - 5x2 = (7
- 5)x2 = 2x2

5b[size=12]2x -
3ay2
-
8b2x + 10ay2 = -3b2x + 7ay2[/size]

Dissimilar or unlike terms in an algebraic
expression cannot be combined when numerical

values have not been assigned to the literal

factors. For example, -5x2 + 3xy - 8y2 contains three dissimilar terms. This expression


cannot be further simplified by combining terms

through addition or subtraction. The expression may be rearranged as x(3y - 5x) -
8y2 or

y(3x - 8y) - 5x2, but such a rearrangement is

not actually a simplification.

Practice problems. Combine like terms in
the following expression:


Answers:

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PostSubject: Re: What is an algebraic expression?   Wed Sep 24, 2008 2:33 pm

syaro pana!!

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PostSubject: Re: What is an algebraic expression?   Wed Sep 24, 2008 3:12 pm

AW. HAHAHAHHA, Mao nay GUIDE>

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