Algebra basic.pdf

DEFINATION :
› The part of mathematics in which letters and other general
symbols are used to represent numbers and quantities in formulae
and equations.
› The word algebra comes from the Arabic ‫الج‬
‫بر‬ [al-jabr] i.e..
‘reunion of broken parts’.
The word algebra comes from the title of a book
by Muhammad ibn Musa al-Khwarizmi.[5]

Early history of algebra :
• The roots of algebra can be traced to the ancient Babylonians, who
developed an advanced arithmetical system with which they were able to
do calculations in an algorithmic fashion. The Babylonians developed
formulas to calculate solutions for problems typically solved today by
using linear equations, quadratic equations, and indeterminate linear
equations.
• In the context where algebra is identified with the theory of equations,
the Greek mathematician Diophantus has traditionally been known as
the "father of algebra" and in the context where it is identified with rules
for manipulating and solving equations

NUMBERREA
REAL NUMBERS R
RATIONAL NUMBERS Q
INTEGERS Z
WHOLE NUMBERS W
NATURAL NUMBERS
N
PRIME
NUMBERS
COMPOSITE
NUMBERS

Set
Natural
numbers N
Integers Z
Rational numbers Q
Real numbers R
Complex numbers C
Integers modulo
3
Z/3Z = {0, 1, 2}
Operation + × + × + − × ÷ + ×
Closed Yes Yes Yes Yes Yes Yes Yes No Yes Yes
Identity 0 1 0 1 0 N/A 1 N/A 0 1
Inverse N/A N/A −a N/A −a N/A
1/a
(a ≠ 0)
N/A
0, 2,
1,
respec
tively
N/A, 1,
2,
respect
ively
Associativ
e
Yes Yes Yes Yes Yes No Yes No Yes Yes
Commutat
ive
Yes Yes Yes Yes Yes No Yes No Yes Yes

Basics of algebra
• EXPONENT
• EXPRESSIONS
• POLYNOMIALS [ MONOMIAL , BINOMIAL , TRINOMIAL
• LIKE TERMS AND UNLIKE TERMS
• CONSTANTS

1. Exponent
2. Numerical
values
3. Terms
4. Operations
5. Constant Term
In the above-given equation, the letters x and y are the unknown variables which
we have to determine. Whereas 3 and 2 are the numerical values. c denotes the
constant term.

EQUATION:
An equation is a statement which implies two same
identities separated by “=” sign. Whereas an
expression is a group of different terms separated
by ‘+’ or ‘-‘ sign.

POLYNOMIALS :
A polynomial is a function that can be
expressed as a sum of terms.
Ex: x2 − 4x + 7

MONOMIAL:
A monomial is a polynomial, which has only one
term. A monomial is an algebraic expression with a
single term but can have multiple variables and a
higher degree too.
For example, 9x ,3 yz .

BINOMIAL:
A binomial is a polynomial or algebraic
expression, which has a maximum of two non-
zero terms. It consists of only two variables.
Ex: 4x2+5y2 , xy2+xy

TRINOMIAL :
A trinomial is a polynomial with three terms.[OR]
A polynomial with three terms is called a
trinomial.
Ex: x2 + 5x - 2, - x2 - 2x - 3,

LIKE AND UNLIKE
TERMS :
Like terms are those
terms which have the
same variable and
same exponent raised
to power.
Unlike terms are
those where the
coefficients are
different in an
algebraic equation

Basic Algebra Operations:
Addition: x + y
Subtraction: x – y
Multiplication: xy
Division: x/y or x ÷ y
where x and y are the variables.
The order of these operations will follow the BODMAS rule, which
means the terms inside the brackets are considered first. Then, roots
and exponents are operated on second priority. Solve all the division
and multiplication operations and later addition and subtraction.

Basic Algebra Formula:
• a2 – b2 = (a – b)(a + b)
• (a+b)2 = a2 + 2ab + b2
• a2 + b2 = (a – b)2 + 2ab
• (a – b)2 = a2 – 2ab + b2
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
• (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc

(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc

Algebra basic.pdf

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Algebra basic.pdf