NCERT Class 9 Maths Lab Manual – Verify the Algebraic Identity a² – b² = (a+b) (a-b)
To verify the algebraic identity a² – b² = (a+b) (a-b).
- Drawing sheet
- Colored papers
- Sketch pen
- Square and its area.
- Rectangle and its area.
- For square and its area refer to Activity 3.
- For rectangle and its area refer to Activity 3.
- Trapezium is a quadrilateral whose two sides are parallel and two sides are non-parallel. In the trapezium ABCD, sides AB and CD are parallel while sides AD and BC are non-parallel.
Area of trapezium =½ (Sum of parallel sides x Distance between parallel sides)
= ½ (AB + CD) x DE
- Cut out a square WQRS of side a units from a coloured paper, (see Fig. 5.2)
- Cut out a square WXYZ of side b units (b < a) from another coloured paper, (see Fig. 5.3)
- Paste the smaller square WXYZ on the bigger square WQRS as shown in Fig. 5.4.
- Join the points Y and R using sketch pen. (see Fig. 5.4)
- Cut out the trapeziums XQRY and ZYRS from WQRS (see Fig. 5.5 and 5.6).
- Paste both trapeziums obtained in step 5th on the drawing sheet as shown in Fig. 5.7
From Fig. 5.2 and Fig. 5.3, we have Area of square WQRS = a²
Area of square WXYZ = b² Now, from Fig. 5.4, we have
Area of square WQRS – Area of square WXYZ = Area of trapezium XQRY + Area of trapezium ZYRS
=Area of rectangle XQZS [from Fig. 5.7]
= XS . SZ [∴ Area of rectangle = Length x Breadth]
So, a² – b² = (a + b) (a – b)
Here, area is in square units.
On actual measurement, we get
a =…….. , b = …….. ,
So, a² =…….. ,
b² = …….. ,
a + b = …….. ,
a-b = …….. ,
a² -b² = …….. ,
and (a + b)(a-b) = …….. ,
Flence, a² – b² = (a + b) (a – b)
The algebraic identity a² – b² = (a + b) (a – b) has been verified.
The identity (a² – b²) = (a + b)(a-b) can be used for
- calculating the difference of squares of two numbers.
- getting some products involving two numbers.
- simplification and factorization of algebraic expressions.
Which algebraic identity should be used to evaluate 64² — 36²?
a² – b² = (a + b) (a – b)
If the sides of a rectangle are (√3 + √2) units and (√3 – √2) units, then what will be its area?
1 sq unit
Is the identity a² – b² = (a + b) (a – b), holds for all real values of a and b?
Is a² – b² a monomial?
No, a² – b² is a binomial because it has two terms.
Find the degree of an identity a² – b² = (a – b) (a + b).
The degree of an identity is two.
Write the places where the algebraic identity a² – b² = (a – b) (a + b) is used.
This identity is used in solving the quadratic equation, mensuration problem, factorisation of polynomial, etc.
The algebraic identity a² – b² = (a- b) (a + b) is true for only natural numbers.
No, it is true for all real numbers.
If we take both negative variables, then their is any effect of algebraic identity.
We know a² – b² = (a + b) (a – b)
Suppose we take a = -a and b = -b,
then (-a)² – (-b)² = (-a – b) (-a + b)
=> a² – b² = (a – b) (a + b)
Is the algebraic identity a² – b² = (a + b) (a – b) also true, if any one of the variable in the given identity is zero?
Yes, suppose b = 0, then
a² – 0² = (a + 0) (0 – 0)
=> a² = a², true.
Verify that (x² – y² ) = (x + y) (x – y) by taking x = 9 and y = 7.