Saturday, 20 May 2017

What is Algebra with the list of Important Algebra Formulas for IBPS PO Exam

In this post, we will discuss one of the fundamental topics of mathematics - Algebra with a list of Algebra Formulas which will help you to solve algebra problems in IBPS PO Exam
Algebra Formulas
Algebra is one of the basic fundamental topics of Mathematics which makes its way in IBPS PO Exam. Algebra problems can’t be ignored from any competitive exams point of view. Algebra problems, though they appear to be complicated, can be simply solved using algebra formulas in seconds. In this post, we will discuss what is algebra and the list of algebra formulas that will help us solve algebra problems in less time.

What is Algebra?

Algebra is a branch of mathematics that deals with equations, utilising letters and other symbols to represent a specific set of numbers, values, vectors, etc., in the description of relations.

Different terms used in Algebra

Variables - When a value or a parameter is unknown then a variable represents the unknown value.
Example: x, y, a, b, $, © etc.

Term – A term can be a single variable or combination of terms.
Example: x, 4, 7y, 3x2 etc.

Expression: An expression is the combination of terms.
Example: 3x2 + 4x + 9, 4x3 – 2x2 + 3x + 2 etc
.
Equation: An equation has ‘=” sign and it always has a solution to the expression.
Example: x + 1 = 4

Basis of Classification
Algebraic expressions can be classified based on the following:

1. Number of Terms:
An expression can be differentiated on the number of terms it includes.

Monomial- An expression having a single term is called as a monomial.
Example: 5x2y

Binomial – An expression having two terms is called as binomial.
Example: 5x2y + 2xy

Polynomial – An expression having more than two terms is called as a polynomial.
Example: 5x2y + 2xy + 3x + xy

2. Degree of the Expression
A degree is defined as the highest or maximum sum of the powers of all the variables in any term of the expression.

Linear Equation - An expression which has a degree of 1 is called a linear Equation.

Quadratic Equation - An expression which has a degree of 2 is called a Quadratic Equation.

Cubic Equation - An expression which has a degree of 3 is called a Cubic Equation.

Operation on Algebraic Equations

I. Addition 
Question: What is the Sum of 3x2 + 5x + 2 and 2x + 1?
Solution:
Step 1:
Collect different groups of like terms.
3x2, 5x and 2x, 2 and 1

Step 2:
Find the sum of like terms
3x² = 3x²
5x + 2x = 7x
2 + 1 = 3

Step 3: Write the final term after addition
3x² + 7x + 3


II. Subtraction
Question: What is the difference between 3x² + 5x + 2 and 2x + 1?
Solution:
Step 1:
Collect different groups of like terms.
3x², 5x and 2x, 2 and 1

Step 2:
Find the difference between of like terms
3x² = 3x²
5x - 2x = 3x
2 - 1 = 1

Step 3: Write the final term, 
3x2 + 3x + 3

III. Multiplication
Question: What is the product of 3x² + 5x + 2 and 2x + 1?
Solution:
Step 1:
Find the product by using the rule the product of two factors with like the sign is positive and the products of two factors with, unlike terms.
i.e.
Algebra Formulas
And using the surds rule, if y is a variable and m, n are positive integer then,
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Now by multiplying the two expressions we get,
(3x² + 5x + 2) (2x + 1) = 3x³ + 3x² + 10x² + 5x + 4x + 2

Step 2:
Add the like terms together
3x³ + 3x² + 10x² + 5x + 4x + 2
= 3x³ + 13x² + 9x + 2
Algebra Formulas
Remainder Theorem
Let f(x) be a polynomial of a degree ≥ 1, and α be any real number, if f(x) is divisible by (x – α), then the remainder is equal to f(α)
Algebra Formulas
Factor Theorem
Let F(x) be a polynomial of a degree ≥ 1, and α be any real number, if F(x) = 0, then  (x-α),is a factor of F(x), then F(x) = 0.

Example: F(x) = x² - 3x - 4 ( ɑ = 4)
F(4) = 4² - 3 x 4 - 4 
F(4) = 16 - 12 - 4
f(4) = 0 
Therfore, (x - 4) is the factore of F(x) = x² - 3x - 4.

Methods of Simplification based on fraction 

When we have two fractions in proportion, we represent them in
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The operations that can be performed on these fractions are

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List of Algebra Formulas that will help you solve Algebra Problems
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Do write down in the comment section how this list of algebra formulas helped you to solve algebra problems. 

Stay tuned for next blog.
 Algebra Formulas
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