**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**

- 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°.

- A rectangle is a quadrilateral whose opposite sides are equal and all the angles are 90°
- 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)

- 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)

- 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)

- 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)

- 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).

- 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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