Introduction to Algebra
Answers
Algebra is one among the oldest branches in the history of mathematics that deals with the number theory, geometry, and analysis. The definition of algebra sometimes states that the study of the mathematical symbols and the rules, and it involves the manipulation of these mathematical symbols. Algebra includes almost everything right from solving elementary equations to the study of the abstractions. Algebra equations are included in many chapters of Maths, which student will learn in their academics. Also, there are several formulas and identities present in algebra.
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Answer:
Explanation:
Introduction to Algebra:-
Preliminary Definitions
In algebra, letters are used to represent numbers. The letters used to represent these numbers are called variables. Combinations of variables and numbers along with mathematical operations form algebraic expressions, or just expressions. The following are some examples of expressions with one variable, x:
2x+3 xsq-9 3xsq+2x-1 (x-5)/(x sq -25)
Terms in an algebraic expression are separated by addition operators, and factors are separated by multiplication operators. The numerical factor of a term is called the coefficient. For example, the algebraic expression
3xsq+2x−1 can be thought of as 3xsq+2x+(−1) and has three terms. The first term, 3xsq, represents the quantity 3⋅x⋅x, where 3 is the coefficient and x is the variable. All of the variable factors, with their exponents, form the variable part of a term. If a term is written without a variable factor, then it is called a constant term. Consider the components of 3xsq+2x−1,
Terms Coefficient Variable Part
3
xsq 3 xsq
2
x 2 x
−1 −1
The third term in this expression, −1, is a constant term because it is written without a variable factor. While a variable represents an unknown quantity and may change, the constant term does not change.
Example 1: List all coefficients and variable parts of each term: 5xsq−4xy-y sq .
.Solution: Think of the third term in this example, −ysq, as −1ysq.
Terms Coefficient Variable Part
5
x
sq 5 x
sq
−4
x
y −4 x
y
−y
sq −1 y
sq
Answer: Coefficients:
{−4,−1,5}
; variable parts:
{xsq,xy,ysq}
Some terms, such as y
sq and −
ysq , appear not to have a coefficient. The multiplicative identity property states that 1 times anything is itself and occurs so often that it is customary to omit this factor and write
1 y sq =y sq
-1y sq = -y sq
Therefore, the coefficient of y sq is actually 1 and the coefficient of −
y sq is −1. In addition, you will encounter terms that have variable parts composed of algebraic expressions as factors.
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