• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Class 9 Maths Lab Manual – Verify the Algebraic Identity (a+b)² = a² + 2ab+b²

NCERT Class 9 Maths Lab Manual – Verify the Algebraic Identity (a+b)² = a² + 2ab+b²

OBJECTIVE

To verify the algebraic identity (a+b)² = a² + 2ab+b².

Materials Required

  1. Drawing sheet
  2. Pencil
  3. Cello-tape
  4. Coloured papers
  5. Cutter
  6. Ruler

Prerequisite Knowledge

  1. Square and its area.
  2. Rectangle and its area.

Theory

  1. A square is a quadrilateral whose all sides are equal and all the angles are 90°.
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 1
  2. A rectangle is a quadrilateral whose opposite sides are equal and all the angles are 90°NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 2
  3. Area of rectangle = Length x Breadth

Procedure

  1. From a coloured paper, cut out a square whose length of each side is a units and name it as square PQRS. (see Fig. 3.3)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 3
  2. From same coloured paper as in step 1st, cut out another square whose length of each side is b units (a > b) and name it as square RFGH. (see Fig 3.4)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 4
  3. From different coloured paper, cut out a rectangle of length a units and breadth b units and name it as rectangle SRHE. (see Fig. 3.5)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 5
  4. From same coloured paper as in step 3rd cut out a rectangle of length b units and breadth a units and name it as rectangle QIFR. (see Fig. 3.6)
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 6
  5. Arrange the above cutted figures (squares and rectangles) as shown in figure and paste it on drawing sheet using cello-tape, (see Fig. 3.7).
    NCERT Class 9 Maths Lab Manual - Verify the Algebraic Identity (a+b)² = a² + 2ab+b² 7
  6. figure, it is clear that we have obtained a square PIGE of side (a + b).

Demonstration
From Fig. 3.7, area of PIGE
= Area of square PQRS + Area of square RFGH + Area of rectangle SRHE + Area of rectangle QIFR
= a² + b² + ab + ba
=  a² + 2ab + b² sq units ,..(i)
Also, PIGE is a square of side (a + b).
So, area of PIGE=  (a+b)² sq units …(ii)
Hence, from Eqs. (i) and (ii), we can write  (a+b)² = a² + 2ab+b² .

Observation
On actual measurement, we get
a = ………… , b = ………… , (a + b) = ………… ,
Now, a² = ………..  , b² = ……….. , ab =  ……….. ,
(a+b)² = ……….. , 2ab = ……….. .
Hence, (a+b)² = a² + 2ab+b² .
The identity may be verified by taking different values of a and b.

Result
The identity  a² + 2ab+b² = (a+b)²  has been verified.

Application
The identity is useful for
1. calculating the square of a number, which can be expressed as the sum of the two convenient numbers.
2. simplification and factorisation of some algebraic expressions.

Viva Voce
Question 1:
What do you mean by algebraic expression?
Answer:
A combination of constants and variables, connected by four fundamental arithmetic operations +, -, x and + is called an algebraic expression.

Question 2:
Are (a+b)² and a² + 2ab+b² algebraic expressions?
Answer:
Yes, both (a+b)² and a² + 2ab+b² are algebraic expressions because they contain both variables (a and b) and arithmetic operations (+).

Question 3:
What is the difference between algebraic expression and polynomial?
Answer:
In algebraic expression, variables may have negative exponents but in polynomial, variables have only positive integer powers.

Question 4:
\sa2 + 2ab+b2 a polynomial?
Answer:
Yes, because the variables a and b have positive integer powers.

Question 5:
Is the identity (a+b)² = a² + 2ab+b² hold for negative values of a and b?
Answer:
Yes, given identity also hold for negative values.

Suggested Activity
Verify this activity by taking
1. a = 2 and b = 3
2. a = 6 and b = 9

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • MCQ Questions with Answers for Class 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1 all Subjects
  • Angle, Types of Angles
  • AND gate is formed by using two? 1)OR 2)NAND 3)NOT 4)NOR
  • And expression for one minus the quotient of one and a number X?
  • What is average human body temperature in Kelvins?
  • How many moles of caffeine are in a cup, and how many molecules of caffeine?
  • How far will the car have traveled in that time?
  • What is its atomic number?
  • How many neutrons does it have?
  • An atom loses electrons to form what?
  • What is the atomic number of this atom?
  • Which one of these is the answer?
  • What is its concentration?
  • Can an equilateral triangle also be isosceles?
  • What is the charge of an alpha particle?

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
cbse ncert
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions