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RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

All you need of Class 8 at this link: Class 8

Question 1: Multiply:
(5x + 3) by (7x + 2)

Answer 1: To multiply, we will use distributive law as follows:
$(5 x + 3) (7 x + 2) = 5 x (7 x + 2) + 3 (7 x + 2) = (5 x \times 7 x + 5 x \times 2) + (3 \times 7 x + 3 \times 2) = (35 x^{2} + 10 x) + (21 x + 6) = 35 x^{2} + 10 x + 21 x + 6 = 35 x^{2} + 31 x + 6$ Thus, the answer is $35 x^{2} + 31 x + 6$ .

Question 2: Multiply:
(2x + 8) by (x − 3)

Answer 2: To multiply the expressions, we will use the distributive law in the following way:
$(2 x + 8) (x - 3) = 2 x (x - 3) + 8 (x - 3) = (2 x \times x - 2 x \times 3) + (8 x - 8 \times 3) = (2 x^{2} - 6 x) + (8 x - 24) = 2 x^{2} - 6 x + 8 x - 24 = 2 x^{2} + 2 x - 24$ Thus, the answer is $2 x^{2} + 2 x - 24$ .

Question 3: Multiply:
(7x + y) by (x + 5y)

Answer 3: To multiply, we will use distributive law as follows:
$(7 x + y) (x + 5 y) = 7 x (x + 5 y) + y (x + 5 y) = 7 x^{2} + 35 x y + x y + 5 y^{2} = 7 x^{2} + 36 x y + 5 y^{2}$
Thus, the answer is $7 x^{2} + 36 x y + 5 y^{2}$ .

Question 4: Multiply:
(a − 1) by (0.1a² + 3)

Answer 4: To multiply, we will use distributive law as follows:
$(a - 1) (0.1 a^{2} + 3) = 0.1 a^{2} (a - 1) + 3 (a - 1) = 0.1 a^{3} - 0.1 a^{2} + 3 a - 3$
Thus, the answer is $0.1 a^{3} - 0.1 a^{2} + 3 a - 3$ .

Question 5: Multiply:
(3x² + y²) by (2x² + 3y²)

Answer 5: To multiply, we will use distributive law as follows:
$(3 x^{2} + y^{2}) (2 x^{2} + 3 y^{2}) = 3 x^{2} (2 x^{2} + 3 y^{2}) + y^{2} (2 x^{2} + 3 y^{2}) = 6 x^{4} + 9 x^{2} y^{2} + 2 x^{2} y^{2} + 3 y^{4} = 6 x^{4} + 11 x^{2} y^{2} + 3 y^{4}$ Thus, the answer is $6 x^{4} + 11 x^{2} y^{2} + 3 y^{4}$ .

Question 6: Multiply:

Answer 6: To multiply, we will use distributive law as follows:

Thus, the answer is

Question 7: Multiply:
(x⁶ − y⁶) by (x²+ y²)

Answer 7: To multiply, we will use distributive law as follows:

(x6−y6)(x2+y2)=x6(x2+y2)−y6(x2+y2)=(x8+x6y2)−(y6x2+y8)=x8+x6y2−y6x2−y8 Thus, the answer is $x^{8} + x^{6} y^{2} - y^{6} x^{2} - y^{8}$ .

Question 8: Multiply:
(x² + y²) by (3a + 2b)

Answer 8: To multiply, we will use distributive law as follows:

(x2+y2)(3a+2b)=x2(3a+2b)+y2(3a+2b)=3ax2+2bx2+3ay2+2by2 Thus, the answer is $3 a x^{2} + 2 b x^{2} + 3 a y^{2} + 2 b y^{2}$ .

Question 9: Multiply:
[−3d + (−7f)] by (5d + f)

Answer 9: To multiply, we will use distributive law as follows:
$[- 3 d + (- 7 f)] (5 d + f) = (- 3 d) (5 d + f) + (- 7 f) (5 d + f) = (- 15 d^{2} - 3 d f) + (- 35 d f - 7 f^{2}) = - 15 d^{2} - 3 d f - 35 d f - 7 f^{2} = - 15 d^{2} - 38 d f - 7 f^{2}$ Thus, the answer is $- 15 d^{2} - 38 d f - 7 f^{2}$ .

Question 10: Multiply:
(0.8a − 0.5b) by (1.5a − 3b)

Answer 10: To multiply, we will use distributive law as follows:
$(0.8 a - 0.5 b) (1.5 a - 3 b) = 0.8 a (1.5 a - 3 b) - 0.5 b (1.5 a - 3 b) = 1.2 a^{2} - 2.4 a b - 0.75 a b + 1.5 b^{2} = 1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ Thus, the answer is $1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ .

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

Question 1: Multiply:
(5x + 3) by (7x + 2)

Question 2: Multiply:
(2x + 8) by (x − 3)

Question 3: Multiply:
(7x + y) by (x + 5y)

Answer 3: To multiply, we will use distributive law as follows:
$(7 x + y) (x + 5 y) = 7 x (x + 5 y) + y (x + 5 y) = 7 x^{2} + 35 x y + x y + 5 y^{2} = 7 x^{2} + 36 x y + 5 y^{2}$
Thus, the answer is $7 x^{2} + 36 x y + 5 y^{2}$ .

Question 4: Multiply:
(a − 1) by (0.1a² + 3)

Answer 4: To multiply, we will use distributive law as follows:
$(a - 1) (0.1 a^{2} + 3) = 0.1 a^{2} (a - 1) + 3 (a - 1) = 0.1 a^{3} - 0.1 a^{2} + 3 a - 3$
Thus, the answer is $0.1 a^{3} - 0.1 a^{2} + 3 a - 3$ .

Question 5: Multiply:
(3x² + y²) by (2x² + 3y²)

Question 6: Multiply:

Answer 6: To multiply, we will use distributive law as follows:

Question 7: Multiply:
(x⁶ − y⁶) by (x²+ y²)

Answer 7: To multiply, we will use distributive law as follows:

Question 8: Multiply:
(x² + y²) by (3a + 2b)

Answer 8: To multiply, we will use distributive law as follows:

Question 9: Multiply:
[−3d + (−7f)] by (5d + f)

Question 10: Multiply:
(0.8a − 0.5b) by (1.5a − 3b)

Answer 10: To multiply, we will use distributive law as follows:
$(0.8 a - 0.5 b) (1.5 a - 3 b) = 0.8 a (1.5 a - 3 b) - 0.5 b (1.5 a - 3 b) = 1.2 a^{2} - 2.4 a b - 0.75 a b + 1.5 b^{2} = 1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ Thus, the answer is $1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ .

Question 11: Multiply:
(2x²y² − 5xy²) by (x² − y²)

Answer 11: To multiply, we will use distributive law as follows:

(2x2y2−5xy2)(x2−y2)=2x2y2(x2−y2)−5xy2(x2−y2)=2x4y2−2x2y4−5x3y2+5xy4 Thus, the answer is

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-4 ) Class 8 Notes | EduRev

Question 1: Multiply:(5x + 3) by (7x + 2)

Answer 1: To multiply, we will use distributive law as follows:(5x+3)(7x+2)=5x(7x+2)+3(7x+2)=(5x×7x+5x×2)+(3×7x+3×2)=(35x2+10x)+(21x+6)=35x2+10x+21x+6=35x2+31x+6Thus, the answer is 35x2+31x+635x2+31x+6.

Question 2: Multiply:(2x + 8) by (x − 3)

Question 3: Multiply:(7x + y) by (x + 5y)

Answer 3: To multiply, we will use distributive law as follows:(7x+y)(x+5y)=7x(x+5y)+y(x+5y)=7x2+35xy+xy+5y2=7x2+36xy+5y27x+yx+5y=7xx+5y+yx+5y=7x2+35xy+xy+5y2=7x2+36xy+5y2Thus, the answer is 7x2+36xy+5y27x2+36xy+5y2.

Question 4: Multiply:(a − 1) by (0.1a2 + 3)

Answer 4: To multiply, we will use distributive law as follows:(a−1)(0.1a2+3)=0.1a2(a−1)+3(a−1)=0.1a3−0.1a2+3a−3a-10.1a2+3=0.1a2a-1+3a-1=0.1a3-0.1a2+3a-3Thus, the answer is 0.1a3−0.1a2+3a−30.1a3-0.1a2+3a-3.

Question 5: Multiply:(3x2 + y2) by (2x2 + 3y2)

Answer 5: To multiply, we will use distributive law as follows:(3x2+y2)(2x2+3y2)=3x2(2x2+3y2)+y2(2x2+3y2)=6x4+9x2y2+2x2y2+3y4=6x4+11x2y2+3y43x2+y22x2+3y2=3x22x2+3y2+y22x2+3y2=6x4+9x2y2+2x2y2+3y4=6x4+11x2y2+3yThus, the answer is 6x4+11x2y2+3y46x4+11x2y2+3y4.

Question 6: Multiply:

Answer 6: To multiply, we will use distributive law as follows:

Question 7: Multiply:(x6 − y6) by (x2 + y2)

Answer 7: To multiply, we will use distributive law as follows:

Question 8: Multiply:(x2 + y2) by (3a + 2b)

Answer 8: To multiply, we will use distributive law as follows:

Question 9: Multiply:[−3d + (−7f)] by (5d + f)

Answer 9: To multiply, we will use distributive law as follows:[−3d+(−7f)](5d+f)=(−3d)(5d+f)+(−7f)(5d+f)=(−15d2−3df)+(−35df−7f2)=−15d2−3df−35df−7f2=−15d2−38df−7f2Thus, the answer is −15d2−38df−7f2-15d2-38df-7f2.

Question 10: Multiply:(0.8a − 0.5b) by (1.5a − 3b)

Answer 10: To multiply, we will use distributive law as follows:(0.8a−0.5b)(1.5a−3b)=0.8a(1.5a−3b)−0.5b(1.5a−3b)=1.2a2−2.4ab−0.75ab+1.5b2=1.2a2−3.15ab+1.5b2Thus, the answer is 1.2a2−3.15ab+1.5b21.2a2-3.15ab+1.5b2.

Question 11: Multiply:(2x2y2 − 5xy2) by (x2 − y2)

Answer 11: To multiply, we will use distributive law as follows:

(2x2y2−5xy2)(x2−y2)=2x2y2(x2−y2)−5xy2(x2−y2)=2x4y2−2x2y4−5x3y2+5xy4 Thus, the answer is

Question 1: Multiply:
(5x + 3) by (7x + 2)

Question 2: Multiply:
(2x + 8) by (x − 3)

Question 3: Multiply:
(7x + y) by (x + 5y)

Answer 3: To multiply, we will use distributive law as follows:
$(7 x + y) (x + 5 y) = 7 x (x + 5 y) + y (x + 5 y) = 7 x^{2} + 35 x y + x y + 5 y^{2} = 7 x^{2} + 36 x y + 5 y^{2}$
Thus, the answer is $7 x^{2} + 36 x y + 5 y^{2}$ .

Question 4: Multiply:
(a − 1) by (0.1a² + 3)

Answer 4: To multiply, we will use distributive law as follows:
$(a - 1) (0.1 a^{2} + 3) = 0.1 a^{2} (a - 1) + 3 (a - 1) = 0.1 a^{3} - 0.1 a^{2} + 3 a - 3$
Thus, the answer is $0.1 a^{3} - 0.1 a^{2} + 3 a - 3$ .

Question 5: Multiply:
(3x² + y²) by (2x² + 3y²)

Question 7: Multiply:
(x⁶ − y⁶) by (x²+ y²)

Question 8: Multiply:
(x² + y²) by (3a + 2b)

Question 9: Multiply:
[−3d + (−7f)] by (5d + f)

Question 10: Multiply:
(0.8a − 0.5b) by (1.5a − 3b)

Answer 10: To multiply, we will use distributive law as follows:
$(0.8 a - 0.5 b) (1.5 a - 3 b) = 0.8 a (1.5 a - 3 b) - 0.5 b (1.5 a - 3 b) = 1.2 a^{2} - 2.4 a b - 0.75 a b + 1.5 b^{2} = 1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ Thus, the answer is $1.2 a^{2} - 3.15 a b + 1.5 b^{2}$ .

Question 11: Multiply:
(2x²y² − 5xy²) by (x² − y²)