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Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions and Identities – Exercise 6.3 | Set 2
  • Last Updated : 06 Apr, 2021

Chapter 6 Algebraic Expressions and Identities  – Exercise 6.3 | Set 1

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 -8x2y6 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 (3.2x6y3) * (2.1x2y2) 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 (5x6) * (-1.5x2y3) * (-12xy2) 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 (2.3a5b2) * ((1.2)a2b2) 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 (-8x2y6) * (-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: (-xy3) * (yx3 ) * (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) * (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)a2b) * ((-2/3)b2c) * ((-7/6)c2a)

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 * b * 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) * (-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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