Expansion of (x + a) (x +b)

Expansion of (x + a) (x +b)

          Which two quantities are to be multiplied ? (x +a) and (x + b). which is the equal term in (x + a) (x + b) ?      ……….. x.

          Which are the unequal terms in the quantities (x + a) and                        (x + b) ?                                       ……. a and b

          Study the following multiplication shown in horizontal arrangement.

(x + a) (x + b)       = x × (x + b) + a × (x + b)

                             = x² + xb + ax + ab

                             = x² + ax + bx + ab

                             = x² + (a + b)x + ab

Which are the terms in the product ?    ……x², (a+b)x and ab

What is the characteristic of the first term ?

………… square of the equal term.

What is the characteristic of the second term ?

…… Sum of the two unequal terms multiplied by the equal term.

What is the characteristic of the third term ?

……..product of the unequal terms.

This can be written in words as follows.

(equal term + first unequal term) (equal term + second unequal term)

= (equal term)² + (sum of unequal terms) × (equal term) + (product of unequal terms)

This gives us the following formula.

(x+a) (x+b) = x² + (a+b)x  + ab

Irrational and Real Numbers

Irrational and Real Numbers

Revision : Rational numbers

         

 The numerators in the numbers , , ,  are integers while their denominators are non-zero integers. Hence, these are rational numbers. If p is any integer and q, any non-zero integer, then,  is a rational number

The decimal form of a rational number

          

Two rational numbers can have different decimal forms. To understand the nature of this difference, let us work out the decimal form of two rational numbers  and , and study them. What is the difference in the decimal forms ?

(1)  The decimal form of .

The decimal form of  is 7.9375

As the remainder in this example is 0, the process of division is complete. Hence, we do not get any digit after 5 in the quotient obtained.

          It means that the decimal form 7.9375 is a terminating one. 

Square roots of numbers

Square roots of numbers

          It is customary not to write ‘+’ sign before a positive number. For example, +10 = 10. 

We shall, henceforth, observe this convention in all discussions.

6 ×  = 36     ∴ 6 is the square root of 36.

Similarly, (-6) × (-6) = 36       ∴ (-6) too is a square root of 36.

          
Thus, 6 and -6 are the two square roots of 36.

         

study the following video lessons:

 In the same way, work out in your mind the pairs of numbers of which 4, 49 and 121 are the squares and write statements like the above.

          What do we learn by observing the numbers and their square roots in the above examples?
we see that –

* Every positive number has two square roots.

* These square roots are opposite numbers of each other.

HOME

We are a rapidly growing company, driven by our passion

for education and commitment to our students.We’re glad you’re joining us!

• what we are covering:
• Engaging Practice: 
• worksheets, interactive exercises, hands-on activities, video lessons and more
• Easy to Use Flashcards: 
• Practice on their own, or with parents and teachers
•  learn every topic with flashcards

Animated presentations and worksheets are included for 

every topic to give you a better understanding.

Each chapter consists of more than 50 slides of Presentation 

and 10 worksheets for every chapter in word doc or jpg.

You can download the courseware at any time and can learn 

it at own pace of time.

Innovatively created content consists the following:

• Animated PPTs/videos are made for each chapter
• Many examples from web based solutions
• New creative ideas
• Worksheets for every topic for the practice exercise
• Online multiple choice questions

Divided topics

flashcards indulge students in mathematics in a very creative manner which does not seem to bore them and at the same point of time teach them the required concepts.

with Colourful pictures, The topics are structured to bring Mathematics to you through interesting examples and exercise - 

you learn the best when you are having funMathematics concepts, without making it a burden

To learn in a playful manner:

A Flash card is a template which showcases a certain problem in 

a very nice way so that students don’t feel burdened by the 

problem and at the same time, they learn to solve that problem 

and the underlying concept in a playful manner.

• Would be useful for parents, teachers, students, and tutors use widely in your classroom practice for daily activities and make it fun and easy

• 
  

We’re glad you’re joining us!

Lowest Common Multiple (LCM)

READ THE LESSON.

GO THROUGH EXAMPLE VIDEO AND

 LET US FIND ANSWER THE QUESTION BELOW

POST YOUR ANSWER BY COMMENTS.

Lowest Common Multiple 

(LCM)

Carefully consider the following numbers that are divisible by 8 and by 12.

Numbers divisible by 8 (i. e. multiples of 8) :

8, 16, 24, 32, 40, 48, 56, 64, 72, …

Numbers divisible by 12 (i. e. multiples of 12) :

12, 24, 36, 48, 60, 72, 84, ….

Here the numbers 24, 48, 72, .. are the common multiples of 8 and 12. 24 is the smallest or the lowest of them all. 

Thus, 24 is the smallest or the lowest common multiple or LCM of  8 and 12.

·       Note that the LCM of relative prime numbers is the product of those numbers. 

Examples:

  Find the LCM :

 65, 39

Greatest Common Divisor (GCD)

READ THE LESSON.

GO THROUGH EXAMPLE VIDEO AND

 LET US FIND ANSWER THE QUESTION BELOW

POST YOUR ANSWER BY COMMENTS.

Greatest Common Divisor (GCD)

let us consider the divisors of 84 and 48.

Divisors of 84 : 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42, 84

Divisors of 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

We find that the underlined factors 1, 2, 3, 4, 6, 12 are present in both groups. They are called common divisors.

Of these common divisors 1, 2, 3, 4, 6, 12 the biggest divisor is 12.

 It is called the greatest common divisor or the GCD for short. It is also called highest common factor or HCF.

view the examples:

Find the GCD :

 120, 96

MATHSEASYWAY FLASHCARDS

Work at your pace through these 

colorful flashcards to learn Mathematics in a fun-filled way!

• Study at your own pace, when you want, as much as you want

• More than 1000 flashcards for primary school students

• Designed for children in 3 years -15 years age group, Junior KG to 8th

• Would be useful for parents, teachers, students, and tutors

• 
  

The workbooks have been carefully and beautifully

 designed by us.

This is an introductory course designed for students

 right from Junior KG to Class 8th.

Here you can work through more than 1000 colorful flashcards

 to understand basic concepts in Mathematics in a fun-filled way.

 Regular books contain a limited number of examples. 

Here you will get a lot of examples. 

Enroll in Maths course

What makes these workbooks unique?

• Colourful pictures
• Colouring pages for kids
• Counting with pictures

Why should you enroll in this course:

• Course is structured to bring Mathematics to you through interesting examples and exercise - you learn the best when you are having fun
• Mathematics concepts, without making it a burden
• This course is specifically designed for students and parents of students, from Junio KG to Grade 5th

What’s in the course:

• Recorded classes which can be downloaded
• Study material/ workbooks which will be provided in PDF format

Course outline:

• Basic Maths skills
• Mind math
• Numbers fun
• Geometry kids
• Tables
• Multiply and divisions
• Addition and subtractions
• Sample pages
• Time
• Money
• Fractions
• Counting
• Algebra
• Geometry