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

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) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=(−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:
$(- 4 x^{2}) \times (- 6 x y^{2}) \times (- 3 y z^{2}) = \{(- 4) \times (- 6) \times (- 3)\} \times (x^{2} \times x) \times (y^{2} \times y) \times z^{2} = \{(- 4) \times (- 6) \times (- 3)\} \times (x^{2 + 1}) \times (y^{2 + 1}) \times z^{2} = - 72 x^{3} y^{3} z^{2}$ Thus, the answer is $- 72 x^{3} y^{3} z^{2}$ .

Question 12: Find each of the following product:

Answer 12: 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:

×(a4×a2)×(b×b2)

×a4+2×b1+2

×a6×b3

=− 3/5 a6b3

Thus, the answer is − 3/5 a6b3

Question 13: Find each of the following product:

Answer 13: 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:

×(a×a×a2)×(b2×b)×(c2×c)

×(a1+1+2)×(b2+1)×(c2+1)

=−a4b3c3

Thus, the answer is $- a^{4} b^{3} c^{3}$ .

Question 14: Find each of the following product:

Answer 14: 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:

(4/3 u2vw)×(−5uvw2)×(1/3 v2wu)

×(u2×u×u)×(v×v×v2)×(w×w2×w)

×(u2+1+1)×(v1+1+2)×(w1+2+1)

=− 20/9 u4v4w4

Thus, the answer is − 20/9 u4v4w4

Question 15: Find each of the following product:
$(0.5 x) \times (\frac{1}{3} x y^{2} z^{4}) \times (24 x^{2} y z)$

Answer 15: 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:

(0.5x)×(1/3 xy2z4)×(24x2yz)

=(0.5×1/3×24)×(x×x×x2)×(y2×y)×(z4×z)

=(0.5×1/3×24)×(x1+1+2)×(y2+1)×(z4+1)

=4x4y3z5

Thus, the answer is $4 x^{4} y^{3} z^{5}$ .

Question 16: Find each of the following product:

(4/3 pq2)×(−1/4 p2r)×(16p2q2r2)43pq2×-14p2r×16p2q2r2

Answer 16: 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:

(4/3 pq2)×(−1/4 p2r)×(16p2q2r2)

={4/3×(−1/4)×16}×(p×p2×p2)×(q2×q2)×(r×r2)

={4/3×(− 1/4)×16}×(p1+2+2)×(q2+2)×(r1+2)

=− 16/3p5q4r3

Thus, the answer is $- \frac{1}{3} p^{5} q^{4} r^{3}$ .

Question 17: Find each of the following product:
(2.3xy) × (0.1x) × (0.16)

Answer 17: 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:
$(2.3 x y) \times (0.1 x) \times (0.16) = (2.3 \times 0.1 \times 0.16) \times (x \times x) \times y = (2.3 \times 0.1 \times 0.16) \times (x^{1 + 1}) \times y = 0.0368 x^{2} y$ Thus, the answer is $0.0368 x^{2} y$ .

Question 18: Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

Answer 18: We have to find the product of the expression in order to express it as a monomial.
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:
$(3 x) \times (4 x) \times (- 5 x) = \{3 \times 4 \times (- 5)\} \times (x \times x \times x) = \{3 \times 4 \times (- 5)\} \times (x^{1 + 1 + 1}) = - 60 x^{3}$
Substituting x = 1 in LHS, we get:
$LHS = (3 x) \times (4 x) \times (- 5 x) = (3 \times 1) \times (4 \times 1) \times (- 5 \times 1) = - 60$ =(3×1)×(4×1)×(−5×1)

=−60
Putting x = 1 in RHS, we get:
$RHS = - 60 x^{3} = - 60 {(1)}^{3} = - 60 \times 1 = - 60$ $∵$ LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is $- 60 x^{3}$ .

Question 19: Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x²) × (−3x) × $(\frac{4}{5} x^{3})$

Answer 19: We have to find the product of the expression in order to express it as a monomial.
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:

(4x2)×(−3x)×(4/5 x3)

={4×(−3)×4/5}×(x2×x×x3)

={4×(−3)×4/5}×(x2+1+3)

=− 48/5x6

$∴$ $(4 x^{2}) \times (- 3 x) \times (\frac{4}{5} x^{3}) = - \frac{48}{5} x^{6}$

$(4 x^{2}) \times (- 3 x) \times (\frac{4}{5} x^{3}) = - \frac{48}{5} x^{6}$

$(4 x^{2}) \times (- 3 x) \times (\frac{4}{5} x^{3}) = - \frac{48}{5} x^{6}$ $(4 x^{2}) \times (- 3 x) \times (\frac{4}{5} x^{3}) = - \frac{48}{5} x^{6}$

$(4 x^{2}) \times (- 3 x) \times (\frac{4}{5} x^{3}) = - \frac{48}{5} x^{6}$

Question 20: Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x⁴) × (x²)³ × (2x)²

Answer 20: We have to find the product of the expression in order to express it as a monomial.

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n} = a^{m + n} and {(a^{m})}^{n} = a^{m n}$ .
We have:
$(5 x^{4}) \times {(x^{2})}^{3} \times {(2 x)}^{2} = (5 x^{4}) \times (x^{6}) \times (2^{2} \times x^{2}) = (5 \times 2^{2}) \times (x^{4} \times x^{6} \times x^{2}) = (5 \times 2^{2}) \times (x^{4 + 6 + 2}) = 20 x^{12}$ ∴ (5x4)×(x²)³×(2x)² =20x¹²

Substituting x = 1 in LHS, we get:
$LHS = (5 x^{4}) \times {(x^{2})}^{3} \times {(2 x)}^{2} = (5 \times 1^{4}) \times {(1^{2})}^{3} \times {(2 \times 1)}^{2} = (5 \times 1) \times (1^{6}) \times {(2)}^{2} = 5 \times 1 \times 4 = 20$

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

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)

Question 12: Find each of the following product:

Answer 12: 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 13: Find each of the following product:

Answer 13: 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 14: Find each of the following product:

Answer 14: 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:

(4/3 u2vw)×(−5uvw2)×(1/3 v2wu)

Question 15: Find each of the following product:(0.5x)×(1/3 xy2z4)×(24x2yz)0.5x×13xy2z4×24x2yz

Answer 15: 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 16: Find each of the following product:

Answer 16: 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 17: Find each of the following product:(2.3xy) × (0.1x) × (0.16)

Answer 17: 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:(2.3xy)×(0.1x)×(0.16)=(2.3×0.1×0.16)×(x×x)×y=(2.3×0.1×0.16)×(x1+1)×y=0.0368x2yThus, the answer is 0.0368x2y0.0368x2y.

Question 18: Express each of the following product as a monomials and verify the result in each case for x = 1:(3x) × (4x) × (−5x)

=−60Putting x = 1 in RHS, we get:RHS =−60x3=−60(1)3=−60×1=−60∵∵ LHS = RHS for x = 1; therefore, the result is correctThus, the answer is −60x3-60x3.

Question 19: Express each of the following product as a monomials and verify the result in each case for x = 1:(4x2) × (−3x) × (4/5 x3)

Answer 19: We have to find the product of the expression in order to express it as a monomial.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 20: Express each of the following product as a monomials and verify the result in each case for x = 1:(5x4) × (x2)3 × (2x)2

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)

Answer 12: 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 13: 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 14: 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 15: Find each of the following product:
$(0.5 x) \times (\frac{1}{3} x y^{2} z^{4}) \times (24 x^{2} y z)$

Answer 15: 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 16: 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 17: Find each of the following product:
(2.3xy) × (0.1x) × (0.16)

Question 18: Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

=−60
Putting x = 1 in RHS, we get:
$RHS = - 60 x^{3} = - 60 {(1)}^{3} = - 60 \times 1 = - 60$ $∵$ LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is $- 60 x^{3}$ .

Question 19: Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x²) × (−3x) × $(\frac{4}{5} x^{3})$

Answer 19: We have to find the product of the expression in order to express it as a monomial.
To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., $a^{m} \times a^{n} = a^{m + n}$ .

Question 20: Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x⁴) × (x²)³ × (2x)²