Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.3 | Set 1

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) * (y^{2 +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) * (b²  *  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 * a²  * 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)

= 0.0368x²y 

Chapter 6 Algebraic Expressions and Identities  – Exercise 6.3 | Set 2