CBSE Class 8

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

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 6E.

Other Exercises

• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

Objective questions :
Tick the correct answer in each of the following :

Question 1.
Solution:

Question 2.
Solution:
(3q + 7p² – 2r³ + 4) – (4p² – 2q + 7r³ – 3)
= 3q + 7p² – 2r³ + 4 – 4p² + 2q – 7r³ + 3
= 5q + 3p² – 9r³ + 7 = 3p² + 5q – 9r³ + 7 (d)

Question 3.
Solution:
(x + 5) (x – 3) = x² + (5 – 3) x + 5 X ( – 3)
= x² + 2x – 15 (d)

Question 4.
Solution:
(2x + 3) (3x – 1)
= 6x² – 2x + 9x – 3
= 6x² + 7x – 3 (b)

Question 5.
Solution:
(x + 4) (x + 4)
= x² + (4 + 4) x + 4 X 4
= x² + 8x + 16 (c)

Question 6.
Solution:
(x – 6) (x – 6)
= x² + ( – 6 – 6) x + ( – 6) ( – 6)
= x² – 12x + 36 (d)

Question 7.
Solution:
(2x + 5) (2x – 5)
= (2x)² – (5)²
= 4x² – 25

Question 8.
Solution:

Question 9.
Solution:
(2x² + 3x + 1) ÷ (x + 1)

= 2x +1 (b)

Question 10.
Solution:
(x² – 4x + 4) ÷ (x – 2)

= x – 2 (a)

Question 11.
Solution:
(a + 1) (a – 1) (a² + 1)
= (a² – 1) (a² + 1)
= a⁴ (c)

Question 12.
Solution:

Question 13.
Solution:
\(\left( { x }+\frac { 1 }{ { x } } \right) =5\)
Squaring on both sides

Question 14.
Solution:
\(\left( { x }-\frac { 1 }{ { x } } \right) =6\)
Squaring on both sides

Question 15.
Solution:
(82)² – (18)²
= (82 + 18) (82 – 18)
= 100 x 64
= 6400 (c)

Question 16.
Solution:
(197 x 203)
= (200 – 3) (200 + 3)
= (200)² – (3)²
= 40000 – 9
= 39991 (a)

Question 17.
Solution:
a + b = 12, ab = 14
a² + b²
= (a + b)² – 2ab
= (12)² – 2 x 14
= 144 – 28
= 16 (b)

Question 18.
Solution:
a – b = 7, ab = 9
a² + b²
= (a – b)² + 2ab
= (7)² + 2 x 9
= 49 + 18
= 67 (a)

Question 19.
Solution:
x = 10
4x² + 20x + 25
= (2x)² + 2 x 2x x 5 + (5)²
= (2x + 5)²
= (2 x 10 + 5)
= (20 + 5)²
= (25)²
= 625 (c)

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

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

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

• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

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

You can also Download NCERT Solutions for Class 8 English to help you to revise complete Syllabus and score more marks in your examinations.

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.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

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

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 6C.

Other Exercises

• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

Question 1.
Solution:
(i) 24x²y³ ÷ 3xy

Question 2.
Solution:
(i)(5m³ – 30m² + 45m) ÷ 5m

Write the quotient and remainder when we divide:

Question 3.
Solution:

Question 4.
Solution:

Quotient = x – 2
Remainder = 0

Question 5.
Solution:

Question 6.
Solution:

Question 7.
Solution:

Question 8.
Solution:

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

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

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

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

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 6B.

Other Exercises

• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

Find each of the following products?

Question 1.
Solution:
(5x + 7) X (3x + 4) = 5x(3x + 4) + 7(3x + 4)
= 15x² + 20x + 21x + 28 = 15x² + 41x + 28 Ans.

Question 2.
Solution:
(4x + 9) X (x – 6) = 4x(x – 6) + 9(x – 6)
= 4x² – 24x + 9x – 54
= 4x² – 15x – 54 Ans.

Question 3.
Solution:
(2x + 5) X (4x – 3) = 2x(4x – 3) + 5(4x – 3)
= 8x² – 6x + 20x – 15
= 8x² + 14x – 15 Ans.

Question 4.
Solution:
(3y – 8) X (5y – 1) = 3y(5y – 1) – 8(5y – 1)
= 15y² – 3y – 40y + 8
= 15y² – 43y + 8 Ans.

Question 5.
Solution:
(7x + 2y) X (x + 4y)
= 7x(x + 4y) + 2y(x + 4y)
= 7x² + 28xy + 2xy + 8y²
= 7x² + 30xy + 8y² Ans.

Question 6.
Solution:
(9x + 5y) X (4x + 3y) = 9x(4x + 3y) + 5y(4x + 3y)
= 36x² + 27xy + 20xy + 15y²
= 36x² + 47xy + 15y² Ans.

Question 7.
Solution:
(3m – 4n) X (2m – 3n)
= 3m(2m – 3n) – 4n(2m – 3n)
= 6m² – 9mn – 8mn + 12n²
= 6m² – 17mn + 12n² Ans.

Question 8.
Solution:
(x² – a²) X (x – a)
= x²(x – a) – a²(x – a)
= x³ – x²a – xa² + a³ Ans.

Question 9.
Solution:
(x² – y²) X (x + 2y)
= x²(x + 2y) – y²(x + 2y)
= x³ + 2x²y – xy² – 2y³ Ans.

Question 10.
Solution:
(3p² + q²) X (2p² – 3q²)
= 3p²(2p² – 3q²) + q²(2p² – 3q²)
= 6p⁴ – 9p²q² + 2p²q² – 3q⁴
= 6p⁴ – 7p²q² – 3q⁴ Ans.

Question 11.
Solution:
(2x² – 5y²) X (x² + 3y²)
= 2x²(x² + 3y²) – 5y²(x² + 3y²)
= 2x⁴ + 6x²y² – 5x²y² – 15y⁴)
= 2x⁴ + x2y² – 15y⁴ Ans.

Question 12.
Solution:
(x³ – y³) X (x² + y²)
= x³(x² + y²) – y³(x² + y²)
= x⁵ + x³y² – x²y³ – y⁵ Ans.

Question 13.
Solution:
(x⁴ + y⁴) X (x² – y²)
= x⁴(x² – y²) + y⁴(x² – y²)
= x⁶ – x⁴y² + x²y⁴ – y⁶ Ans.

Question 14.
Solution:
\(\left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \times \left( { x+ }\frac { 1 }{ { x } } \right)\)

Find each of the following products:

Question 15.
Solution:
(x² – 3x + 7) X (2x + 3)
= (x² – 3x + 7) (2x) + (x² – 3x + 7) X 3
= 2x³ – 6x + 14x + 3x² – 9x + 21
= 2x³ – 3x² + 5x + 21 Ans.

Question 16.
Solution:
(3x² + 5x – 9) X (3x – 5)
= 3x²(3x – 5x) + 5x(3x – 5) – 9(3x – 5)
= 9x³ – 15x² + 15x² – 25x – 27x + 45
= 9x³ – 52x + 45 Ans.

Question 17.
Solution:
(x² – xy + y²) X (x + y)
= (x² – xy + y²) X x + (x² – xy + y²) X y
= x³ – x²y + xy² + x²y – xy² + y³
= x³ + y³ Ans.

Question 18.
Solution:
(x² + xy + y²) X (x – y)
(x² + xy + y²) X x + (x² + xy + y²) X ( – y)
= x³ + x²y + xy² – x²y – xy² – y³
= x³ – y³ Ans.

Question 19.
Solution:
(x³ – 2x² + 5) X (4x – 1)
= (x³ – 2x² + 5) X 4x + (x³ – 2x² + 5) X ( – 1)
= 4x⁴ – 8x³ + 20x – x³ + 2x² – 5
= 4x⁴ – 9x³ + 2x² + 20x – 5 Ans.

Question 20.
Solution:
(9x² – x + 15) X (x² – 3)
(9x² – X + 15) X x² + (9x² – x + 15) X ( – 3)
= 9x⁴ – x³ + 15x² – 27x² + 3x – 45
= 9x⁴ – x³ – 12x² + 3x – 45 Ans.

Question 21.
Solution:
(x² – 5x + 8) X (x² + 2)
= (x² – 5x + 8) X x² + (x² – 5x + 8) X 2
= x⁴ – 5x³ + 8x² + 2x² – 10x + 16
= x⁴ – 5x³ + 10x² – 10x + 16 Ans.

Question 22.
Solution:
(x³ – 5x² + 3x + 1) X (x² – 3)
= (x³ – 5x² + 3x + 1) X x² + (x³ – 5x² + 3x + 1) X ( – 3)
= x⁵ – 5x⁴ + 3x³ + x² – 3x³ + 15x² – 9x – 3
= x⁵ – 5x⁴ + 16x² – 9x – 3 Ans.

Question 23.
Solution:
(3x + 2y – 4) X (x – y + 2)

Question 24.
Solution:
(x² – 5x + 8) X (x² + 2x – 3)

Question 25.
Solution:
(2x² + 3x – 7) X (3x² – 5x + 4)

Question 26.
Solution:
(9x² – x + 15) X (x² – x – 1)

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

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

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

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 6A.

Other Exercises

• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
• RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

Add:

Question 1.
Solution:
8ab + ( – 5ab) + (3ab) + ( – ab)
= 8ab – 5ab + 3ab – ab = 11 ab – 6ab
= 5ab Ans.

Question 2.
Solution:
7x + ( – 3x) + 5x + ( – x) + ( – 2x)
= 7x – 3x + 5x – x – 2x
= 12x – 6x = 6x Ans.

Question 3.
Solution:

Question 4.
Solution:

Question 5.
Solution:

Question 6.
Solution:

Question 7.
Solution:

Question 8.
Solution:

Subtarct:

Question 9.
Solution:
-5a²b – 3a²b = – 8a²b Ans.

Question 10.
Solution:
6pq – ( – 8pq) = 6pq + 8pq

Question 11.
Solution:
– 8abc – ( – 2abc)
= – 8abc + 2abc
= – 6abc Ans.

Question 12.
Solution:
– 11p – ( – 16p)
= – 11p + 16p
= 5p Ans.

Question 13.
Solution:

Question 14.
Solution:

Question 15.
Solution:

Question 16.
Solution:

Question 17.
Solution:

Question 18.
Solution:

Question 19.
Solution:
Let length of rectangle = 5x² – 3y²
and breadth = x² + 2xy
Perimeter = 2(Length + Breadth)
= 2(5x² – 3y² + x² + 2xy)
= 2(6x² – 3y² + 2xy)
= 12x² – 6y² + 4xy Ans.

Question 20.
Solution:
Perimeter of a triangle = 6p² – 4p + 9
Sum of two sides of it = 3p² – 5p + 3 + p² – 2p + 1 = 4p² – 7p – 4
Third side = (6p² – 4p + 9) – (4p² – 7p + 4)
= 6p² – 4p + 9 – 4p² + 7p – 4
= 2p² + 3p + 5 Ans

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

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.