Alegbra - ALGEBRAIC EXPRESSIONS An algebraic expression is...

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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. 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 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 - 3x 2 + 7x + 1 is a polynomial of four terms. The trinomial x 2 + 2x + 1 is an example of a polynomial which has a special name. 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) COMBINING TERMS 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: 7x 2 - 5x 2 = (7 - 5)x 2 = 2x 2 5b 2 x - 3ay 2 - 8b 2 x + 10ay 2 = -3b 2 x + 7ay 2 Combine like terms in the following expression: Answers:
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SYMBOLS OF GROUPING The following example shows how the rule for removal of parentheses is applied to algebraic expressions: 2a - (-4x + 3by) = 2a + 4x - 3by Parenthesis preceded by a plus sign can be removed without any other changes, m the following example shows: 2b + (a -b)=2b+a-b-a+b Enclosing Terms in Parentheses When it is desired to enclose a group of terms in parentheses, the group of terms remains unchanged if the sign preceding the parentheses is positive. This is illustrated as follows: Note that this agrees with the rule for removing parentheses preceded by a plus sign. If terms are enclosed within parentheses preceded by a minus sign, the signs of all the terms enclosed must be changed as in the following example: In problems 1 .through 4, remove the symbols of grouping and combine like terms. In problems 5 through 8, enclose the first two terms in parentheses preceded by a plus sign (understood) and the last two in parentheses preceded by a minus sign. EXPONENTS AND RADICALS Thus the general form can be expressed as follows: n a . n b = n a+b The algebraic rules for radicals also remain the same as those of arithmetic. In arithmetic,
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Alegbra - ALGEBRAIC EXPRESSIONS An algebraic expression is...

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