Class 8 RD Sharma Mathematics Solutions Chapter 6 Algebraic Expressions and Identities Exercise 6.3 | Set 2 (original) (raw)
Last Updated : 23 Jul, 2025
Chapter 6 of RD Sharma's Class 8 Mathematics textbook titled "Algebraic Expressions and Identities" dives into the foundational concepts of the algebra. This chapter is essential for the building a strong understanding of the algebraic expressions, identities and their applications. Exercise 6.3 | Set 2 focuses on the simplifying algebraic expressions and solving problems that require the application of the various algebraic identities.
Algebraic Expressions and Identities
The Algebraic expressions are mathematical phrases that include the numbers, variables and operators. They represent the values that can change depending on the variables involved. Identities on the other hand, are equations that are true for the all values of the variables within them. These identities help simplify complex algebraic expressions and solve equations more efficiently. Some common identities include the (a+b)2=a2+2ab+b2 and (a−b)2=a2−2ab+b2.
Class 8 RD Sharma Mathematics Solutions - Exercise 6.3 | Set 2
**Explain each of the products as monomials and verify the result in each case for x = 1
**Question 18: (3x) * (4x) * (-5x)
**Solution:
First, separate the numbers and variables.
= (3 * 4 * -5) * (x * x * x)
Add the powers of the same variable and multiply the numbers.
= (-60) * (x1+1+1)
= -60x3
**Verification:
LHS = (3x) * (4x) * (-5x)
Putting x = 1 in LHS we get,
= (3 * 1) * (4 * 1) * (-5 * 1)
= 3 * 4 * -5
= -60
RHS = -60x3
Putting x = 1 in RHS we get,
= -60 * (1)3
= -60
LHS = RHS
Hence, verified.
**Question 19: (4x2) * (-3x) * ((4/5)x3)
**Solution:
First separate the numbers and variables.
= (4 * -3 * (4/5)) * (x2 * x * x3)
Add the powers of the same variable and multiply the numbers.
= (-48/5) * (x2+1+3)
= (-48/5)x6
**Verification:
LHS = (4x2) * (-3x) * ((4/5)x3)
Putting x = 1 in LHS we get,
= (4 * 1) * (-3 * 1) * ((4/5) * 1)
= 4 * -3 * (4/5)
= (-48/5)
RHS = (-48/5)x6
Putting x = 1 in RHS we get,
= (-48/5) * (1)6
= -(48/5)
LHS = RHS
Hence, verified.
**Question 20: (5x4) * (x2 )3 * (2x)2
**Solution:
First separate the numbers and variables.
= (5 * 4) * (x4 * x6 * x2)
Add the powers of the same variable and multiply the numbers.
= (20) * (x4+6+2)
= (20)x12
**Verification:
LHS = (5x4) * (x2)3 * (2x)2
Putting x = 1 in LHS we get,
= (5 * (1)4) * ((12))3 * (2 * 1)2
= (5 * 1) * (1)3 * (2)2
= 5 * 1 * 4
= 20
RHS = (20)x12
Putting x = 1 in RHS we get,
= (20) * (1)12
= 20
LHS = RHS
Hence, verified.
**Question 21: (x2 )3 * (2x) * (-4x) * (5)
**Solution:
First separate the numbers and variables.
= (2 *-4 * 5) * (x6 * x * x)
Add the powers of the same variable and multiply the numbers.
= (-40) * (x6+1+1)
= (-40)x8
**Verification:
LHS = (x2)3 * (2x) * (-4x) * (5)
Putting x = 1 in LHS we get,
= (1)6 * (2 * 1) * (-4 * 1) * (5)
= 1 * 2 * -4 * 5
= -40
RHS = (-40)x8
Putting x = 1 in RHS we get,
= (-40) * (1)8
= -40
LHS = RHS
Hence, verified.
**Question 22: Write down the product of -8x 2 y 6 **and -20xy. Verify the product for x = 2.5, y = 1.
**Solution:
(-8x2y6 ) * (-20xy)
First separate the numbers and variables.
= (-8 * -20) * (x2 * x) * (y6 * y)
Add the powers of the same variable and multiply the numbers.
= 160 * (x2+1) * (y6+1)
= 160x3y7
**Verification:
LHS = (-8x2y6) * (-20xy)
Putting x = 2.5 and y = 1 in LHS we get,
= (-8 * (2.5)2 * (1)6) * (-20 * 2.5 * 1)
= (-8 * 6.25 * 1) * (-20 * 25)
= -50 * -50
= 2500
RHS = 160x3y7
Putting x = 2.5 and y = 1 in RHS we get,
= -160 * (2.5)3 * (1)7
= -160 * 15.625
= 2500
LHS = RHS
Hence, verified.
**Question 23: Evaluate (3.2x 6 y 3 ) * (2.1x 2 y 2 ) when x = 1 and y = 0.5.
**Solution:
First, separate the numbers and variables.
= (3.2 * 2.1) * (x6 * x2) * (y3 * y2)
Add the powers of the same variable and multiply the numbers.
= 6.72 * (x6+2) * (y3+2)
= 6.72x8y5
Putting x = 1 and y = 0.5 in the result we get
= 6.72 * (1)8 * (0.5)5
= 6.72 * 0.03125
= 0.21
**Question 24: Find the value of (5x 6 ) * (-1.5x 2 y 3 ) * (-12xy 2 ) when x = 1, y = 0.5.
**Solution:
First, separate the numbers and variables.
= (5 * -1.5 * -12) * (x6 * x2 * x) * (y3 * y2)
Add the powers of the same variable and multiply the numbers.
= 90 * (x6+2+1) * (y3+2)
= 90x9y5
Putting x = 1 and y = 0.5 in the result we get
= 90 * (1)9 * (0.5)5
= 90 * 1 * 0.03125
= 2.8125
**Question 25: Evaluate when (2.3a 5 b 2 ) * ((1.2)a 2 b 2 ) when a = 1 and b = 0.5.
**Solution:
First, separate the numbers and variables.
= (2.3 * 1.2) * (a5 * a2) * (b2 * b2)
Add the powers of the same variable and multiply the numbers.
= 2.76 * (a5+2) * (b2+2)
= 2.76a7b4
Putting a = 1 and b = 0.5 in the result we get
= 2.76 * (1)7 * (0.5)4
= 2.76 * 1 * 0.0625
= 0.1725
**Question 26: Evaluate for (-8x 2 y 6 ) * (-20xy) when x = 2.5 and y = 1.
**Solution:
First, separate the numbers and variables.
= (-8 * -20) * (x2 * x) * (y6 * y)
Add the powers of the same variable and multiply the numbers.
= 160 * (x2+1) * (y6+1)
= 160x3y7
Putting x = 2.5 and y = 1 in the result we get
= 160 * (2.5)3 * (1)7
= 160 * 15.625 * 1
= 2500
**Express each of the following products as monomials and verify the result for x = 1, y = 2: (27 - 31)
**Question 27: (-xy 3 ) * (yx 3 ****) * (xy)**
**Solution:
First separate the numbers and variables.
= (-1 * 1 * 1) * (x * x3 * x) * (y3 * y * y)
Add the powers of the same variable and multiply the numbers.
= -1 * (x1+3+1 ) * (y3+1+1)
= -x5y5
**Verification:
LHS = (-xy3) * (yx3) * (xy)
Putting x = 1 and y = 2 in LHS we get,
= (-1 * (2)3) * (2 * (1)3 ) * (1 * 2)
= -8 * 2 * 2
= -32
RHS = -x5y5
Putting x = 1 and y = 2 in RHS we get,
= -1 * (1)5 * (2)5
= -32
LHS = RHS
Hence, verified.
**Question 28: ((1/8) x2y4) * ((1/4) x4y2 ) * (xy) * (5)
**Solution:
First, separate the numbers and variables.
= ((1/8) * (1/4) * 1 * 5) * (x2 * x4 * x) * (y4 * y2 * y)
Add the powers of the same variable and multiply the numbers.
= (5/32) * (x2+4+1) * (y4+2+1)
= (5/32)x7 y7
**Verification:
LHS = ((1/8) x2y4) * ((1/4) x4y2) * (xy) * (5)
Putting x = 1 and y = 2 in LHS we get,
= ((1/8) * (1)2 * (2)4) * ((1/4) * (1)4 * (2)2) * (1 * 2) * (5)
= 2 * 1 * 2 * 5
= 20
RHS = (5/32)x7y7
Putting x = 1 and y = 2 in RHS we get,
= (5/32) * (1)7 * (2)7
= (5/32) * (128)
= 20
LHS = RHS
Hence, verified
**Question 29: (2/5)a2b * (-15b2ac) * ((-1/2)c2)
**Solution:
First, separate the numbers and variables.
= ((2/5) * (-15) * (-1/2)) * (a2 * a) * (b* b2) * (c * c2)
Add the powers of the same variable and multiply the numbers.
= 3 * (a2+1) * (b1+2 ) * (c1+2)
= 3a3b3c3
This expression does not contain x and y . Hence the result cannot be verified for x = 1 and y = 2.
**Question 30: ((-4/7)a 2 b) * ((-2/3)b 2 c) * ((-7/6)c 2 a)
**Solution:
First separate the numbers and variables.
= ((-4/7) * (-2/3) * (-7/6)) * (a2 * a) * (b* b2) * (c * c2)
Add the powers of the same variable and multiply the numbers.
= (-4/9) * (a2+1) * (b1+2) * (c1+2)
= (-4/9)a3b3c3
This expression does not contain x and y . Hence the result cannot be verified for x = 1 and y = 2.
**Question 31: ((4/9)abc3) * ((-27/5)a3b2) * (-8b3c)
**Solution:
First, separate the numbers and variables.
= ((4/9) * (-27/5) * (-8)) * (a * a3) * (b * b2 * b3) * (c3 * c)
Add the powers of the same variable and multiply the numbers.
= (96/5) * (a1+3) * (b1+2+3) * (c3+1)
= (96/5)a4b6c4
This expression does not contain x and y. Hence, the result cannot be verified for x = 1 and y = 2.
**Evaluate each of the following when x = 2 and y = -1.
**Question 32: (2xy) * ((x2y) /4) * (x2) * (y2)
**Solution:
First, separate the numbers and variables.
= (2 * (1/4)) * (x * x2 * x2) * (y * y * y2)
Add the powers of the same variable and multiply the numbers.
= (1/2) * (x1+2+2) * (y1+1+2)
= (1/2)x5y4
Putting x = 2 and y = -1 in the result we get,
= (1/2) * ( 2)5 * (-1)4
= 16
**Question 33: (3/5)x2y * ((-15/4) * x * y2) * ((7/9) x2y2)
**Solution:
First, separate the numbers and variables.
= ((3/5) * (-15/4) * (7/9)) * (x2 * x * x2) * (y * y2 * y2)
Add the powers of the same variable and multiply the numbers.
= (-7/4) * (x2+1+2) * (y1+2+2)
= (-7/4)x5y5
Putting x = 2 and y = -1 in the result we get,
= (-7/4) * ( 2)5 * (-1)5
= -56
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Conclusion
Exercise 6.3 | Set 2 of Chapter 6 enhances students' skills in working with the algebraic expressions and identities. Mastering these concepts is crucial for the progressing to the more advanced topics in algebra. By practicing these problems students will develop a deeper understanding of how to the simplify expressions and apply identities effectively.