RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Class 8: RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The document RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
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Question 1:Write the following squares of binomials as trinomials:
(i) (x + 2)2
(ii) (8a + 3b)2
(iii) (2m + 1)2

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x) (a2b − bc2)

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

(xii) (x2 − ay)

Answer 1: We will use the identities (a+b)2=a2+2ab+b2 and (ab)2=a22ab+b2a+b2=a2+2ab+b2 and a-b2=a2-2ab+b2 to convert the squares of binomials as trinomials.

(i) (x+2)2=x2+2×x×2+b2=x2+4x+b2

(ii) (8a+3b)2=(8a)2+2(8a)(3b)+(6b)2=64a2+48ab+36b2(iii) (2m+1)2=(2m)2+2(2m)(1)+12=4m2+4m+1

(iv) (9a+1/6)2=(9a)2+2(9a)(1/6)+(1/6)2=81a2+3a+1/36

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(x) (a2bbc2)2=(a2b)22(a2b)(bc2)+(bc2)2=a4b22a2b2c2+b2c4 RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(xii) (x2ay)2=(x2)22x2(ay)+(ay)2=x42x2ay+a2y2

Question 2: Find the product of the following binomials:
(i) (2x + y)(2x + y)
(ii) (a + 2b)(a − 2b)
(iii) (a2 + bc)(abc)

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(vi) (2a3 + b3)(2a3 − b3) 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer 2: (i) We will use the identity (a+b)2=a2+2ab+b2a+b2=a2+2ab+b2  in the given expression to find the product.
(2x+y)(2x+y)=(2x+y)2=(2x)2+2(2x)(y)+y2=4x2+4xy+y2(ii) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product.
(a+2b)(a2b)=a2(2b)2=a24b2 (iii) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product.
(a2+bc)(a2bc)=(a2)2(bc)2=a4b2c2 (iv)We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product. 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(v) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product. 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

(vi) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product.
(2a3+b3)(2a3b3)=(2a3)2(b3)2=4a6b6 (vii) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product. 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

(viii) We will use the identity (a+b)(ab)=a2b2a+ba-b=a2-b2 in the given expression to find the product. 

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-5 ) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

Question 3: Using the formula for squaring a binomial, evaluate the following:
(i) (102)2
(ii) (99)2
(iii) (1001)2
(iv) (999)2
(v) (703)2

Answer 3: (i) Here, we will use the identity (a+b)2=a2+2ab+b2a+b2=a2+2ab+b2
(102)2=(100+2)2=(100)2+2×100×2+22=10000+400+4=10404 (ii) Here, we will use the identity (ab)2=a22ab+b2a-b2=a2-2ab+b2
(99)2=(1001)2=(100)22×100×1+12=10000200+1=9801 (iii) Here, we will use the identity (a+b)2=a2+2ab+b2a+b2=a2+2ab+b2
(1001)2=(1000+1)2=(1000)2+2×1000×1+12=1000000+2000+1=1002001 (iv) Here, we will use the identity (ab)2=a22ab+b2a-b2=a2-2ab+b2
(999)2=(10001)2=(1000)22×1000×1+12=10000002000+1=998001 (v) Here, we will use the identity (a+b)2=a2+2ab+b2a+b2=a2+2ab+b2
(703