Question

how to verify class 9 maths lab manuel activity 3
Verify the algebraic identity : (a+b)²= a²+2ab+b².​

Answer 1

Answer:

Step-by-step explanation:

Materials Required

Drawing sheet

Pencil

Cello-tape

Coloured papers

Cutter

Ruler

Prerequisite Knowledge

Square and its area.

Rectangle and its area.

Theory

A square is a quadrilateral whose all sides are equal and all the angles are 90°.

Pic  1

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

Area of rectangle = Length x Breadth

Procedure

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)

Pic  3

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)

Pic  4

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)

Pic 5

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)

Pic 6

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).

Pic 7

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.