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Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.3 | Set 1
  • Last Updated : 26 Nov, 2020

Find each of the following products:

Question 1: 5x2 * 4x3

Solution: 

First, separate the numbers and variables. 

= (5 * 4) * (x2 * x3

Add the powers of the same variable and multiply the numbers.

= 20 * (x2+3)



= 20x5

Question 2: -3a2 * 4b4

Solution: 

First, separate the numbers and variables.

= (-3 * 4) * (a2) * (b4)

= -12a2b4

Question 3: (-5xy) * (-3x2yz)

Solution:  

First separate the numbers and variables.  

= (-5 * -3) * (x * x2) * (y * y) * (z)



Add the powers of the same variable and multiply the numbers.

= 15 * (x1+2) * (y1+1) * (z)

= 15x3y2z

Question 4: (1/2)xy * (2/3)x2yz2

Solution: 

First separate the numbers and variables.  

= ((1/2) * (2/3)) * (x * x2) * (y * y) * (z2)

Add the powers of the same variable and multiply the numbers.

= (1/3) * (x1+2) * (y1+1) * (z2)

= (1/3)x3y2z2

Question 5: ((-7/5)xy2z) * ((13/3)x2yz2)

Solution: 

First separate the numbers and variables.  

= ((-7/5) * (13/3)) * (x * x2) * (y2 * y) * (z * z2)

Add the powers of the same variable and multiply the numbers.

= (-91/15) * (x1+2) * (y2 +1)  *  (z1+2)

= (-91/15)x3y3z3

Question 6:  (( -24/25 )x3z) * ((-15/16 )xz2y)

Solution: 

First separate the numbers and variables. 

= ((-24/25) * (-15/16)) * (x3 * x) * (z * z2) * (y) 

Add the powers of the same variable and multiply the numbers.

= (9/4) * (x3+1) * (z1+2) * (y)

= (9/10)x4yz3

Question 7: ((-1/27)a2b2) * ((9/2))a3b2c2)

Solution: 

First separate the numbers and variables. 

= ((-1/27)) * (9/2)) * (a2 * a3) * (b b2) * (c2)

Add the powers of the same variable and multiply the numbers.

= (-1/6) * (a2+3) * (b2+2) * (c2)

= (-1/6)a5b4c2

Question 8: (-7xy) * ((1/4)x2yz)

Solution:  

First separate the numbers and variables. 

= (-7 * (1/4)) * (x * x2) * (y * y) * (z)

Add the powers of the same variable and multiply the numbers.

= (-7 * (1/4)) * (x1+2) * (y1+1) * (z)

= (-7/4) x3y2z

Question 9: (7ab) * (-5ab2c) * (6abc2)

Solution:  

First separate the numbers and variables. 

= (7 * -5 * 6) * (a * a * a) * (b * b2 * b) * (c * c2)

Add the powers of the same variable and multiply the numbers.

= -210 * (a1+1+1) * (b1+2+1) * (c1+2)

= -210a3b4c3

Question 10: (-5a) * (-10a2) * (-2a3)

Solution: 

First separate the numbers and variables. 

= (-5 * -10 * -2) * (a * a * a3)

Add the powers of the same variable and multiply the numbers.

= (-100) * (a1+2+3)

= -100a6 

Question 11: (-4x2) * (-6xy2) * (3yz2)

Solution: 

First separate the numbers and variables.

= (-4 * -6 * 3) * (x2 * x) * (y2 * y) * (z2)

Add the powers of the same variable and multiply the numbers.

= -72 * (x2+1) * (y2+1) * (z2)

= -72x3y3z2

Question 12: ((-2/7 )a4) * ((-3/4 )a2b) * ((-14/5 )b2)

Solution: 

First separate the numbers and variables.

= ((-2/7) * (-3/4) * (-14/5)) * (a4  * a2) * (b * b2)

Add the powers of the same variable and multiply the numbers.

= (-3/5) * (a4+2) * (b1+2)

= (-3/5)a6b3

Question 13: ((7/9)ab2) * ((15/7) ac2b) * ((-3/5)a2c)

Solution:  

First separate the numbers and variables.

= ((7/9) * (15/7) * (-3/5)) * (a * a * a2) * (b2 * b) * (c2 * c)

Add the powers of the same variable and multiply the numbers.

= (-1) * (a1+1+2) * (b2+1) * (c2+1)

= -a4b3c3

Question 14: ((4/3)u2vw) * (-5uvw2) * ((1/3)v2wu)

Solution: 

First separate the numbers and variables.

= ((4/3) * (-5) * (1/3)) * (u2  * u * u) * (v * v * v2) * (w * w2 * w)

Add the powers of the same variable and multiply the numbers.

= (-20/9) * (u2+1+1) * (v1+1+2) * (w1+2+1)

= (-20/9)u4v4w4

Question 15: (0.5x) * ((1/3) xy2z4) * (24x2yz)

Solution:  

First separate the numbers and variables.

= ((0.5) * (1/3) * (24)) * (x * x * x2) * (y2 * y) * (z4 * z)

Add the powers of the same variable and multiply the numbers.

= (4) * (x1+1+2) * (y2+1) * (z4+1)

= 4x4y3z5

Question 16: ((4/3)pq2) * ((-1/4)p2r) * (16p2q2r2)

Solution: 

First separate the numbers and variables.

= (( 4/3) * (-1/4) * (16)) * (p * p2 * p2) * (q2  * q2) * (r * r2)

Add the powers of the same variable and multiply the numbers.

= (-16/3) * (p1+2+2) * (q2+2) * (r1+2)

= (-16/3)p5q4r3

Question 17: (2.3xy ) * ( 0.1x )  * ( 0.16 )

Solution: 

First separate the numbers and variables.

= (2.3 * 0.1 * 0.16) *  (x * x) * (y)

Add the powers of the same variable and multiply the numbers.

= 0.0368 * (x1+1) * (y)

= 0.0368x2

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