NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.5 in Hindi and English Medium updated for CBSE session 2022-2023.

## 8th Maths Exercise 9.5 Solution in Hindi and English Medium

### Class 8 Maths Chapter 9 Exercise 9.5 Solution

Grade VIII Mathematics textbook Ex. 9.5 Algebraic Expressions and Identities in PDF file format updated for new academic session 2022-23. PDF solutions and Videos are based on latest NCERT Books for 2022-23 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 NCERT chapter 9 Class 8 Maths.

Class: 8 | Mathematics |

Chapter: 9 | Exercise: 9.5 |

Chapter Name: | Algebraic Expressions and Identities |

Content Type: | PDF and Videos solution |

Medium: | Hindi and English Medium |

#### 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)Â² = aÂ² + 2ab + bÂ².

We have:

Proof:

(a + b)Â² = (a + b) (a + b)

= a(a + b) +b(a + b)

= aÂ² + ab + ba + bÂ²

= aÂ² + 2ab + bÂ²

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

(3x + 2y) (3x +2y)

= (3x + 2y)Â²

= (3x + 2y)Â² = 9xÂ²+ 12xy + 4yÂ² (By identity 1)

##### Identity 2

(a – b)Â² = (aÂ² – 2ab + bÂ²)

Proof:

(a – b)Â² = (a – b) (a – b)

= a(a – b) – b(a – b)

= aÂ² – ab – ba + bÂ²

= aÂ² – 2ab + bÂ²

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

(x – 7y) (4x – 7y)

= 4x X (4x – 7y) â€“ 7y X (4x – 7y)

= 16xÂ² â€“ 28xy â€“ 28xy + 49yÂ²

= 16xÂ² â€“ 56xy + 49yÂ²

##### Identity 3

(a + b) (a – b) = aÂ² – bÂ²

= a(a – b) + b(a – b)

= aÂ² – ab + ba – bÂ²

= aÂ² – bÂ²

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

(4x + 5y) (4x – 5y)

= 4x X (4x – 5y) + 5y X (4x – 5y)

= 16xÂ² -20xy + 20xy â€“ 20yÂ²

= 16xÂ² â€“ 20yÂ²

###### Identities

- (i) (a + b)Â² = aÂ² + 2ab + bÂ².
- (ii) (a – b)Â² = (aÂ² – 2ab + bÂ²)
- (iii) (a + b) (a – b) = aÂ² – bÂ²

### What are the identities of polynomials given in exercise 9.5 of class 8 Maths?

In class 8 Maths exercise 9.5 Polynomial identities are equations that are true for all possible values of the variable. For example, xÂ²+2x+1 = (x+1)Â² is an identity.

### How do you differentiate between identity and formula in exercise 9.5 of 8th Maths?

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.

### What do you learn about equation identity in exercise 9.5 of class 8 Maths?

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

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.