## RS Aggarwal Class 8 Solutions Chapter 6 Operations on Algebraic Expressions Ex 6D

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D.

Other Exercises

Question 1.
Solution:
(i)(x + 6)(x + 6)
= (x + 6)2

Question 2.
Solution:
(i) (x – 4)(x – 4)
= (x – 4)2

Question 3.
Solution:
(i)(8a + 3b)2
= (8a)2 + 2 x 8a x 3b + (3b)2

Question 4.
Solution:
(i)(x + 3)(x – 3)
= (x)2 – (3)2

Question 5.
Solution:
(i) (54)2
= (50 + 4)2

Question 6.
Solution:
(i) (69)2
= (70 – 1)2

Question 7.
Solution:
(i)(82)2 – (18)2
= (82 – 18)(82 – 18)

Question 8.
Solution:
9x2 + 24x + 16
= (3x)2 + 2 x 3x x 4 + (4)2
= (3x + 4)2
= (3 x 12 + 4)2
= (36 + 4)2
= (40)2
= 1600 Ans.

Question 9.
Solution:
64x2 + 81y2 + 144xy = (8x)2 + (9y)2 + 2 x 8x x 9y
= (8x + 9y)2
= $${ \left( 8\times 11+9\times \frac { 4 }{ 3 } \right) }^{ 2 }$$
= (88 + 12)2
= (100)2
= 10000 Ans.

Question 10.
Solution:
(36x2 + 25y2 – 60xy)
= (6x)2 + (5y)2 – 2 x 6x x 5y
= (6x – 5y)2
= $${ \left( 6\times \frac { 2 }{ 3 } -5\times \frac { 1 }{ 5 } \right) }^{ 2 }$$
= (4 – 1)2
= (3)2 = 9

Question 11.
Solution:
$$\left( x+\frac { 1 }{ 4 } \right) =4$$
Squaring on both sides

Question 12.
Solution:
$$\left( x-\frac { 1 }{ x } \right) =5$$
(i) Squaring on both sides

Question 13.
Solution:
(i) (x + 1) (x – 1) (x2 + 1)
= {(x)2 – (1)2} (x2 + 1)
= (x2 – 1) (x2 + 1)
= (x2)2 – (1)2 = x4 – 1 Ans.
(ii) (x – 3) (x + 3) (x2 + 9)
= {(x)2 – (3)2 } (x2 + 9)
= (x2 – 9) (x2 + 9)
= (x2)2 – (9)2 = x4 – 81 Ans.
(iii) (3x – 2y) (3x + 2y) (9x2 + 4y2)
= {(3x)2 – (2y)2} (9x2 + 4y2)
= (9x2 – 4y2) (9x2 + 4y2)
= (9x2)2 – (4y2)2
= 81x4 – 16y4 Ans.
(iv) (2p + 3) (2p – 3) (4p2 + 9)
= {(2p)2 – (3)2} (4p2 + 9)
= (4p2 – 9) (4p2 + 9)
= (4p2)2 – (9)2 = 16p4 – 81 Ans.

Question 14.
Solution:
x + y = 12
Squaring both sides,
(x + y)2 = (12)2
=> x2 + y2 + 2xy = 144
=> x2 + y2 + 2 x 14 = 144
=> x2 + y2 + 28 = 144
=> x2 + y2 = 144 – 28 = 116
x2 + y2 = 116 Ans.

Question 15.
Solution:
x – y = 7
Squaring both sides,
(x – y)2 = (7)2
=> x2 + y2 – 2xy = 49
=> x2 + y2 – 2 x 9 = 49
=> x2 + y2 – 18 = 49
=> x2 + y2 = 49 + 18 = 67
x2 + y2 = 67 Ans.

Hope given RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D are helpful to complete your math homework.

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