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RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-2) 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-2) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-2) 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: Find each of the following product:
5x²× 4x³

Answer 1: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices. However, use of these laws are subject to their applicability in the given expressions.
In the present problem, to perform the multiplication, we can proceed as follows:
$5 x^{2} \times 4 x^{3} = (5 \times 4) \times (x^{2} \times x^{3})$
$= 20 x^{5}$ ( $∵$ $a^{m} \times a^{n} = a^{m + n}$ )
Thus, the answer is $20 x^{5}$ .

Question 2: Find each of the following product:
−3a² × 4b⁴

Answer 2: To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, $a^{m} \times a^{n} = a^{m + n}$ , wherever applicable.
We have:
$- 3 a^{2} \times 4 b^{4} = (- 3 \times 4) \times (a^{2} \times b^{4}) = - 12 a^{2} b^{4}$ Thus, the answer is $- 12 a^{2} b^{4}$ .

Question 3: Find each of the following product:
(−5xy) × (−3x²yz)

Answer 3: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, $a^{m} \times a^{n} = a^{m + n}$ , wherever applicable.
We have:
$(- 5 x y) \times (- 3 x^{2} y z) = \{(- 5) \times (- 3)\} \times (x \times x^{2}) \times (y \times y) \times z = 15 \times (x^{1 + 2}) \times (y^{1 + 1}) \times z = 15 x^{3} y^{2} z$ Thus, the answer is $15 x^{3} y^{2} z$ .

Question 4: Find each of the following product:

Answer 4: To multiply algebraic expressions, we use commutative and associative laws along with the the law of indices, that is, $a^{m} \times a^{n} = a^{m + n}$ .

We have:

Thus, the answer is 1/6 $\frac{1}{6} x^{3} y^{2} z^{2}$ $\frac{1}{6} x^{3} y^{2} z^{2}$ .

Question 5: Find each of the following product:

Answer 5: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .

We have:

(x×x2)×(y2×y)×(z×z2)

×(x1+2)×(y2+1)×(z1+2)

= - 91/15 x3y3x3

Thus, the answer is = - 91/15 x3y3x3

Question 6: Find each of the following product:

Answer 6: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .

We have:

×(x3×x)×(z×z2)×y

×(x3+1)×(z1+2)×y

$= \frac{9}{10} x^{4} y z^{3}$

Thus, the answer is $= \frac{9}{10} x^{4} y z^{3}$

Question 7: Find each of the following product:

Answer 7:To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:

(a2×a3)×(b2×b2)×c2

(a2+3)×(b2+2)×c2

= - 1/6 a5b4c2

Thus, the answer is = - 1/6 a5b4c2

Question 8: Find each of the following product:

Answer 8: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-2) Class 8 Notes | EduRev

=(−7×1/4)×(x×x2)×(y×y)×z

=(−7×1/4)×(x1+2)×(y1+1)×z

=− 7/4 x3y2z

Thus, the answer is − 7/4 x3y2z

Question 9: Find each of the following product:
(7ab) × (−5ab²c) × (6abc²)

Answer 9: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have: (7ab)×(−5ab2c)×(6abc2)={7×(−5)×6}×(a×a×a)×(b×b2×b)×(c×c2)={7×(−5)×6}×(a1+1+1)×(b1+2+1)×(c1+2)=−210a3b4c3 Thus, the answer is $- 210 a^{3} b^{4} c^{3}$ .

Question 10: Find each of the following product:
(−5a) × (−10a²) × (−2a³)

Answer 10: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:
$(- 5 a) \times (- 10 a^{2}) \times (- 2 a^{3}) = \{(- 5) \times (- 10) \times (- 2)\} \times (a \times a^{2} \times a^{3}) = \{(- 5) \times (- 10) \times (- 2)\} \times (a^{1 + 2 + 3}) = - 100 a^{6}$ Thus, the answer is $- 100 a^{6}$ .

Question 11: Find each of the following product:
(−4x²) × (−6xy²) × (−3yz²)

Answer 11: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:
$(- 4 x^{2}) \times (- 6 x y^{2}) \times (- 3 y z^{2}) = \{(- 4) \times (- 6) \times (- 3)\} \times (x^{2} \times x) \times (y^{2} \times y) \times z^{2} = \{(- 4) \times (- 6) \times (- 3)\} \times (x^{2 + 1}) \times (y^{2 + 1}) \times z^{2} = - 72 x^{3} y^{3} z^{2}$

RD Sharma Solutions for Class 8 Math Chapter 6 - Algebraic Expressions and Identities (Part-2) 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-2) Class 8 Notes | EduRev

Question 1: Find each of the following product:5x2 × 4x3

Question 2: Find each of the following product:−3a2 × 4b4

Answer 2: To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, am×an=am+nam×an=am+n, wherever applicable.We have:−3a2×4b4=(−3×4)×(a2×b4)=−12a2b4-3a2×4b4=-3×4×a2×b4=-12a2Thus, the answer is −12a2b4-12a2b4.

Question 3: Find each of the following product:(−5xy) × (−3x2yz)

Question 4: Find each of the following product:

Answer 4: To multiply algebraic expressions, we use commutative and associative laws along with the the law of indices, that is, am×an=am+nam×an=am+n.

Question 5: Find each of the following product:

Answer 5: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.

Question 6: Find each of the following product:

Answer 6: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.

Question 7: Find each of the following product:

Answer 7:To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.We have:

Question 8: Find each of the following product:

Answer 8: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.We have:

Question 9: Find each of the following product:(7ab) × (−5ab2c) × (6abc2)

Question 10: Find each of the following product:(−5a) × (−10a2) × (−2a3)

Question 11: Find each of the following product:(−4x2) × (−6xy2) × (−3yz2)

Answer 11: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.We have:(−4x2)×(−6x

Question 1: Find each of the following product:
5x²× 4x³

Question 2: Find each of the following product:
−3a² × 4b⁴

Question 3: Find each of the following product:
(−5xy) × (−3x²yz)

Answer 4: To multiply algebraic expressions, we use commutative and associative laws along with the the law of indices, that is, $a^{m} \times a^{n} = a^{m + n}$ .

Answer 5: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .

Answer 6: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .

Answer 7:To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:

Answer 8: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .
We have:

Question 9: Find each of the following product:
(7ab) × (−5ab²c) × (6abc²)

Question 10: Find each of the following product:
(−5a) × (−10a²) × (−2a³)

Question 11: Find each of the following product:
(−4x²) × (−6xy²) × (−3yz²)