NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.5

NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.5 (Ex. 9.5) Algebraic Expressions and Identities in PDF file format updated for CBSE academic session 2020-2021. PDF solutions and Videos are based on latest NCERT Books for 2020-21 and all the questions are done in simplified way.

Class 8 Math exercise 9.5 contains the questions based on identities. Most of the questions are to verify the equations using identities. So we have to learn properly all the identities of chapter 9 Class 8 Maths.

Class 8 Maths Chapter 9 Exercise 9.5 Solution

Class: 8Mathematics
Chapter: 9Algebraic Expressions and Identities
Exercise: 9.5PDF and Videos solution

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Class 8 Maths Chapter 9 Exercise 9.5 Solution in Videos

Class 8 Maths Chapter 9 Exercise 9.5 Solution
Class 8 Maths Chapter 9 Exercise 9.5 Explanation

Some Special Products (Special Identities)

An identity is an equality, which is true for all values of the variables.

The following three identities are very important:
Identity 1:

(a + b)² = a² + 2ab + b².
We have:
Proof:
(a + b)² = (a + b) (a + b)
= a(a + b) +b(a + b)
= a² + ab + ba + b²
= a² + 2ab + b²

Find the following product: (3x + 2y) (3x +2y)

(3x + 2y) (3x +2y)
= (3x + 2y)²
= (3x + 2y)² = 9x²+ 12xy + 4y² (By identity 1)

Identity 2:

(a – b)² = (a² – 2ab + b²)
Proof:
(a – b)² = (a – b) (a – b)
= a(a – b) – b(a – b)
= a² – ab – ba + b²
= a² – 2ab + b²

Find the following product: (4x – 7y) (4x – 7y)

(x – 7y) (4x – 7y)
= 4x X (4x – 7y) – 7y X (4x – 7y)
= 16x² – 28xy – 28xy + 49y²
= 16x² – 56xy + 49y²

Identity 3:

(a + b) (a – b) = a² – b²
= a(a – b) + b(a – b)
= a² – ab + ba – b²
= a² – b²

Find the following product: (4x + 5y) (4x – 5y)

(4x + 5y) (4x – 5y)
= 4x X (4x – 5y) + 5y X (4x – 5y)
= 16x² -20xy + 20xy – 20y²
= 16x² – 20y²

We may write these identities as:

(i) (a + b)² = a² + 2ab + b².
(ii) (a – b)² = (a² – 2ab + b²)
(iii) (a + b) (a – b) = a² – b²



What are the identities of polynomials?

Polynomial identities are equations that are true for all possible values of the variable. For example, x²+2x+1= (x+1)² is an identity.

What is difference between identity and formula?

An identity is an equation that is true for all values of the variables. … But there are a lot of them (see trig identities). Formula is a mathematical relationship or rule expressed in symbols.

Which equation is an identity?

Which equation is an identity?An identity equation is an equation that is always true for any value substituted into the variable.

Are all identities equations?

An Identity is an equation that is true for all values (of x). An Equation is only true for certain values (of x).
Example:
(a + b)2 = a + 2ab + b is an identity (and also an equation) because it is true for any values of a and b.

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