## RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.4

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 6.4

Other Exercises

Find the following products

Question 1.
2a3 (3a + 5b)
Solution:
2a3 (3a + 5b) = 2a3 x 3a + 2a3 x 5b
= 6a3 +1 + 10a3b
= 6a4 + 10a3b

Question 2.
-11a (3a + 2b)
Solution:
-11a (3a + 2b) = -11a x 3a – 11a x 2b
= -33a2– 22ab

Question 3.
-5a (7a – 2b)
Solution:
-5a (7a – 2b) = -5a x 7a- 5a x (-2b)
= -35a2 + 10ab

Question 4.
-11y2 (3y + 7)
Solution:
-11y2 (3y + 7) = -11y2 x 3y – 11y2 x 7
= -33y2+1-77y2
= 33y3-77y2

Question 5.
$$\frac { 6x }{ 5 }$$ (x3+y3)
Solution: Question 6.
xy (x3-y3)
Solution:
xy (x3 – y3) =xy x x3 – xy x y3
= x1 + 3 x y – x x y1+3
= x4y – xy4

Question 7.
0.1y (0.1x5 + 0.1y)
Solution:
0.1y (0.1x5 + 0.1y) = 0.1y x 0.1x5 + 0.1y x 0.1y
= 0.01x5y + 0.01y2

Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11.
5x (10x2y – 100xy2)
Solution:
5x (10x2y – 100xy2)
= 1.5x x 10x2y – 1.5x x 100xy2
= 15x1 + 2y- 150x1+1 x y2
15 x3y- 150xy2

Question 12.
4.1xy (1.1x-y)
Solution:
4.1xy (1.1x-y) = 4.1xy x 1.1x – 4.1xy x y
= 4.51x2y-4.1xy2

Question 13. Solution: Question 14. Solution: Question 15.
$$\frac { 4 }{ 3 }$$ a (a2 + 62 – 3c2)
Solution:  Question 16.
Find the product 24x2 (1 – 2x) and evaluate its value for x = 3.
Solution:
24x2 (1 – 2x) = 24x2 x 1 + 24x2 x (-2x)
= 24x2 + (-48x2+1)
= 24x2 – 48x3
If x = 3, then
= 24 (3)2 – 48 (3)3
= 24 x 9-48 x 27 = 216- 1296
= -1080

Question 17.
Find the product of -3y (xy +y2) and find its value for x = 4, and y = 5.
Solution:
-3y (xy + y2) = -3y x xy – 3y x y2
= -3xy2 -3y2 +1  = -3xy2 – 3y3
If x = 4, y = 5, then
= -3 x 4 (5)2 – 3 (5)3 = -12 x 25 – 3 x 125
= -300 – 375 = – 675

Question 18.
Multiply – $$\frac { 3 }{ 2 }$$ x2y3 by (2x-y) and verify the answer for x = 1 and y = 2.
Solution:  Question 19.
Multiply the monomial by the binomial and find the value of each for x = -1, y = 25 and z =05 :
(i) 15y2 (2 – 3x)
(ii) -3x (y2 + z2)
(iii) z2 (x – y)
(iv) xz (x2 + y2)
Solution:  Question 20.
Simplify :
(i) 2x2 (at1 – x) – 3x (x4 + 2x) -2 (x4 – 3x2)
(ii) x3y (x2 – 2x) + 2xy (x3 – x4)
(iii) 3a2 + 2 (a + 2) – 3a (2a + 1)
(iv) x (x + 4) + 3x (2x2 – 1) + 4x2 + 4
(v) a (b-c) – b (c – a) – c (a – b)
(vi) a (b – c) + b (c – a) + c (a – b)
(vii) 4ab (a – b) – 6a2 (b – b2) -3b2 (2a2 – a) + 2ab (b-a)
(viii) x2 (x2 + 1) – x3 (x + 1) – x (x3 – x)
(ix) 2a2 + 3a (1 – 2a3) + a (a + 1)
(x) a2 (2a – 1) + 3a + a3 – 8
(xi) $$\frac { 3 }{ 2 }$$-x2 (x2 – 1) + $$\frac { 1 }{4 }$$-x2 (x2 + x) – $$\frac { 3 }{ 4 }$$x (x3 – 1)
(xii) a2b (a – b2) + ab2 (4ab – 2a2) – a3b (1 – 2b)
(xiii )a2b (a3 – a + 1) – ab (a4 – 2a2 + 2a) – b (a3– a2 -1)
Solution:
(i) 2x2 (x3 -x) – 3x (x4 + 2x) -2 (x4 – 3x2)
= 2xx x3-2x2x x-3x x x4-3x x 2x-2x4 + 6x2
= 2x2 + 3– 2x2 +1 – 3x,1+ 4-6x,1+1 -2x4 + 6x2
= 2x5 – 2x3 – 3x5 — 6x2 – 2x4 + 6x2
= 2x5 – 3x5 – 2a4 – 2x3 + 6x2 – 6x2
= -x5 – 2x4 – 2x3 + 0
= -x5-2x4-2x3
(ii) x3y (x2 – 2x) + 2xy (x3 – x4)
= x3y x x2 – x3y x 2x + 2ay x ac3 – 2xy x x4
= x3 + 2y-2x3 + 1 y + 2x1 + 3y – 2yx4+1
= x5y – 2x4y + 2x4y – 2yx5
= -x5y
(iii) 3a2 + 2 (a + 2) – 3a (2a + 1)
= 3a2 + 2a + 4 – 6a2 – 3a
= 3a2 – 6a2 + 2a – 3a + 4
= -3a2 – a + 4
(iv) x (x + 4) + 3x (2x2 – 1) + 4x2 + 4
= x2 + 4x + 3x x 2x2 – 3x x 1 + 4x2 + 4
= x2 + 4x + 6x2 +1 – 3x + 4x2 + 4
= x2 + 4x + 6x3 – 3x + 4x2 + 4
= 6a3 + 4x2 + x2 + 4x – 3x + 4
= 6x3 + 5x2 + x + 4
(v) a (b – c)-b (c – a) – c (a – b)
= ab – ac – be + ab – ac + bc
= 2ab – 2ac
(vi) a (b – c) + b (c – a) + c (a – b)
= ab – ac + bc – ab + ac – bc
= ab – ab + bc – be + ac – ac
= 0
(vii) 4ab (a – b) – 6a2 (b – b2) -3b2 (2a2 – a) + 2ab (b – a)
= 4a2b – 4ab2 – 6a2b + 6a2b2 – 6a2b2 + 3ab2 + 2ab2 – 2a2b
= 4a2b- 6a2b – 2 a2b – 4ab2 + 3 ab2 + 2ab2 + 6a2b2 – 6a2b2
= 4a2b – 8a2b – 4ab2 + 5 ab2 + 0
= – 4a2b + ab2
(viii) x2 (x2 + 1) – x3 (x + 1) – x (x3 – x)
= x2 + 2 + x2 – x3 + 1 – x3 – x1 + 3 + x1 + 1
= x4 + x2-x4-x3-x4 + x2
= x4-x4-x4-x3 + x2 + x2
= -x4 – x3 + 2x2
(ix) 2a2 + 3a (1 – 2a3) + a (a + 1)
= 2a2 + 3 a – 3 a x 2a3 + a2 + a
= 2a2 + 3a – 6a1 + 3 + a2 + a
= 2a2 + 3a – 6a4 + a2 + a
= -6a4 + 3a2 + 4a
(x) a2 (2a – 1) + 3a + a3 – 8
= 2 a2 x a – a2 x 1+3a + a3-8
= 2a3 – a2 + 3a + a3 – 8
= 2a3 + a3 – a2 + 3a – 8
= 3a3 – a2 + 3a – 8 (xii) a2b (a – b2) + ab2 (4ab – 2a2) – a3b (1 – 2b)
= a2b x a – a2b x b1 + ab2 x 4ab – ab1 x2a2 -a3b x 1 + a3b x 2b
= a2+1 b-a2b2 +1+ 4a1 +1 b2 +1 -2a2+1 b2-a3b + 2a3b1 +1
= a’b – a2b3 + 4a2b3 – 2a3b2 – a3b + 2a3b2
= a3b – a3b – a2b3 + 4a2b3 – 2a3b2 + 2a3b2
= 0 + 3a2b3 + 0 = 3 a2b3
(xiii) a2b (a3 – a + 1) – ab (a4 – 2a2 + 2a) – b (a3 -a2– 1)
= a2b x a3 – a2b x a + a2b – ab x a2 + ab x 2a2 – ab x 2a- ba3 + ba2 + b
= a2+ 3b – a2+1 b + a2b -a1 + 4b + 2a1 + 2b- 2a1+1 b- a3b + a2b + b
= a5b – a3b + a26 – a5b + 2a3b – 2a2b – a3b + a2b + b
= a5b – a3b + 2a3b – a36 – a3b + a2b – 2a2b + a2b + b
= a3b – a5b + 2a3b – 2a3b + 2a2b-2a2b + b
= 0 + 0 + 0 + b = b

Hope given RD Sharma Class 8 Solutions Chapter 6 Algebraic Expressions and Identities Ex 6.4 are helpful to complete your math homework.

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