## RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3

Other Exercises

Find each of the following products (1-8)
Question 1.
5x2 x 4x3
Solution:
5x2 x 4x3 = 5 x 4 x x2 x x3
= 20x2 + 3 = 20xs

Question 2.
3a2 x 4b4
Solution:
-3a2 x 4b4 = -3 x 4 x a2b4
= -12a2b4

Question 3.
(-5xy) x (-3x2yz)
Solution:
(-5xy) x (-3x2yz)
= (-5) x (-3)xy x x2yz
= 15x1 + 2xy1+ 1z= 15x3y2z

Question 4. Solution:  Question 5. Solution: Question 6. Solution:

Question 7. Solution:  Question 8. Solution: Find each of the following products : (9-17)

Question 9.
(7ab) x (-5ab2c) x (6abc2)
Solution:
(7ab) x (-5ab2c) x (6abc2)
= 7 x (-5) x 6 x a x a x a x b x b2 x b x c x c2
=-210 x a1+1+1 x b1+2+1x c1+2
=-210 x a3b4c3

Question 10.
(-5a) x (-10a2) x (-2a3)
Solution:
(-5a) x (-10a2) x (-2a3)
= (-5) (-10) (-2) x a x a2 x a3
= -100a1 + 2 + 3 = -100a6

Question 11.
(-4x2) x (-6xy2) x (-3yz2)
Solution:
(-4x2) x (-6xy2) x (-3yz2)
= (-4) x (-6) x (-3) x2 x x x y2 x y xz2
= -72x2+1 x y2+1 x z2
= 72x3y3z3

Question 12. Solution: Question 13. Solution: Question 14. Solution: Question 15. Solution: Question 16. Solution:  Question 17.
(2.3xy) x (0.1x) x (0.16)
Solution:
(2.3xy) x (0.1x) x (0.16)
= 2.3 x 0.1 x 0.16 x x x x x y
= 0.0368x1 +1 x y = 0.0368x2y

Express each of the following products as a monomials and verify the result in each case for x = 1 : (18 -26)

Question 18.
(3x) x (4x) x (-5x)
Solution: Question 19. Solution:  Question 20.
(5x4) x (x2)3 x (2x)2
Solution:
(5x4) x (x2)3 x (2x)2
= 5x4 x x2 x 3 x 2x x 2x
= 5x4 * x6 x 4x2 = 5 x 4 x x4 + 6 + 2
= 20x12
Verification:
L.H.S. = (5x4) x (x2)3 x (2x)2
= 5 x (1)4 x [(1)2]3 x (2 x 1)2
= 5 x 1 x (1)2 x 3x (2)2
= 5 x 16 x 22 = 5 x 1 x 4 = 20
R.H.S. = 20x12 = 20 (1)12 = 20 x 1 = 20
∴ L.H.S. = R.H.S.

Question 21.
(x2)3 x (2x) x (-4x) x 5
Solution:
(x2)3 x (2x) x (-4x) x (5)
= x2 x 3 X 2x X (-4x) X 5
= x6 x 2x x (-4x) x 5 = 2 x (-4) x 5x6+1 +1
= -40x8
Verification
L.H.S. = (x2)3 x (2x) x (-4x) x (5)
= (12)3 x (2 x 1) x (-4 x 1) x 5
= 1x 2 x (- 4) x 5 = 16 x 2 x (-4) x 5
= 1 x 2 x (-4) x 5 = -40
R.H.S. = -40x8 = -40 x (1)8
= -40 x 1 = -40
∴ L.H.S. = R.H.S.

Question 22.
Write down the product of -8x2y6 and – 20xy Verify the product for x = 2.5, y = 1.
Solution:
Product of -8x2y6 and -20xy
= (-8x2y6) x (-20xy)
= -8 x (-20) x2 x x x y6 x y = 160x2 + 1 x y6 + 1
= 160x3y3
Verification.
L.H.S. = (-8x2y6) x (-20xy)
= -8 x (2.5)2 x (1) x (-20 x 2.5 x 1)
= -8 x 6.25 x 1 x -20 x 2.5
= (-50) x (-50) = 2500
R.H.S. = 160 x = 160 (2.5)3 x (1)7
= 160 x 15.625 x 1 =2500
∴ L.H.S. = R.H.S.

Question 23.
Evaluate : (3.2x6y3) x (2.1x2y2) when x = 1 and y = 0.5.
Solution:
3.2x6y3 x 2.1x2y2
= 3.2 x 2.1 x x6+2 x y3+2
= 6.72x8y5 = 6.72 x (1)8 x (0.5)5
= 6.72 x 1 x 0.03125
= 0.21

Question 24.
Find the value of (5x6) x (-1.5x2y3) x (-12xy2) when x = 1, y = 0.5.
Solution: Question 25.
Evaluate : (2.3a5b2) x (1.2a2b2) when a = 1, b = 0.5.
Solution: Question 26.
Evaluate : (-8x2y6) x (-20xy) for x = 2.5 and y = 1.
Solution: Express each of the following products as a monomials and verify the result for x = 1,y = 2: (27-31)

Question 27.
(-xy3) x (yx3) x (xy)
Solution:
(-xy3) x (yx3) x (xy)
= -x x xx x x yx y x y = -x1 + 3 + 1 x y3 + 1 + = -x5y5
Verification:
L.H.S. = (-xy3) x (yx3) x (xy)
= (-1 x 23) x [2 x (1)3] x (1 X 2)
= (-1 x 8) x (2 x 1) x (1 x 2)
= -8 x 2 x 2 = -32
R.H.S. =-x5y5  = -(1)5 (2)5
= -1 x 32 =-32
∴ L.H.S. = R.H.S.

Question 28. Solution:  Question 29. Solution: Question 30. Solution: Question 31. Solution:  Question 32. Solution:  Question 33. Solution: Hope given RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.3 are helpful to complete your math homework.

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