## Table of Contents

#### Exercise 8.5 class 8 solution-Introduction

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#### Exercise 8.5 class 8 solution : what are Algebric identities ?

Algebraic identities are mathematical expressions that describe relationships between algebraic expressions, variables, and constants. These identities are used in algebra to simplify and manipulate equations and expressions. Here are some common algebraic identities:

**Distributive Property**:

- a(b+c)=ab+ac
- a(b−c)=ab−ac

**Commutative Property**:

- a+b=b+a (addition)
- ab=ba (multiplication)

**Associative Property**:

- (a+b)+c=a+(b+c)(addition)
- (ab)c=a(bc) (multiplication)

**Identity Property**:

a+0=a (addition)

a⋅1=a (multiplication)

**Inverse Property**:

a+(−a)=0 (addition)

a⋅1/a=1 (multiplication, for a≠0)

These identities are fundamental in algebra and are used to simplify expressions, factor polynomials, and solve equations. They are essential tools for solving a wide range of mathematical problems.

#### Exercise 8.5 class 8 solution -Examples of the exercise.

**8.5.1. using identity find (107)^2**

*solve.To find 107^2 using an algebraic identity, you can use the following identity:*

**Example 8.5.2. (x-3y)^2**

**Solve.** To expand the expression (x−3y)^2, you can use the algebraic identity for squaring a binomial.

**Example 8.5.3.** **Using identity solve the following :(3+2n) (3-2n)**

**Solve**.You can solve the expression (3+2n)(3−2n)using the identity (a+b)(a−b)=a^2−b^2.

In this case, let a=3 and b=2n and then apply the identity:

(3+2n)(3−2n)= (3)^2−(2n)^2

Now, subtract the second term from the first term:

= 9−4n

So, using the identity (a+b)(a−b)=a^2−b^2

you can simplify (3+2n)(3−2n) to 9−4n.

**Example 8.5.4. using identity (x+a)(x+b)=x^2+(a+b)x+ab. find 104*107**

Solve.(104 *107) = (100+4 )(100+7)

Now x=100,a=4 , b=7 Then, express the product as follows:

(100+4)(100+7)=(100^2+(4+7)100+4⋅7

Now, use the identity:

100^2+(4+7)100+4⋅7=1002+11⋅100+28

Now, calculate each part:

100^2=10,000,

11⋅100=1100 ,

28

Now, add these values together:

10,000+1,100+28=11,128

So, using the identity, (100+4)(100+7)=11,128

#### Exercise 8.5 class 8 solution- exercise preview

Our Exercise 8.5 Preview is designed to give you a taste of what’s in store. You’ll find a selection of math problems and questions that challenge your analytical and problem-solving skills. It’s a glimpse into the wonderful world of math exercises that will not only sharpen your mathematical prowess but also help you build the confidence you need to excel in your Class 8 studies.

#### Exercise 8.5 class 8 solution- solution pdf

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