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Verify the Algebraic Identity (a+b)² = a² + 2ab+b² Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify the Algebraic Identity (a+b)² = a² + 2ab+b² are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

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

Determine Verify the Algebraic Identity (a+b)² = a² + 2ab+b² Class 9 Practical

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

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NCERT Class 9 Maths Lab Manual