Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 6 Operations On Algebraic Expressions are provided here with simple step-by-step explanations. These solutions for Operations On Algebraic Expressions are extremely popular among Class 8 students for Math Operations On Algebraic Expressions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 6 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 84:
Question 1:
Add:
8ab, −5ab, 3ab, −ab
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
________
Page No 84:
Question 2:
Add:
7x, −3x, 5x, −x, −2x
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
_____
Page No 84:
Question 3:
Add:
3a − 4b + 4c, 2a + 3b − 8c, a − 6b + c
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
___________
Page No 84:
Question 4:
Add:
5x − 8y + 2z, 3z − 4y − 2x, 6y − z − x and 3x − 2z − 3y
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Page No 84:
Question 5:
Add:
6ax − 2by + 3cz, 6by − 11ax − cz and 10cz − 2ax − 3by
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
Page No 84:
Question 6:
Add:
2x3 − 9x2 + 8, 3x2 − 6x − 5, 7x3 − 10x + 1 and 3 + 2x − 5x2 − 4x3
Answer:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Page No 84:
Question 7:
Add:
6p + 4q − r + 3, 2r − 5p − 6, 11q − 7p + 2r − 1 and 2q − 3r + 4
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise:
Page No 84:
Question 8:
Add:
4x2 − 7xy + 4y2 − 3, 5 + 6y2 − 8xy + x2 and 6 − 2xy + 2x2 − 5y2
Answer:
On arranging the terms of the given expressions in the descending powers of and adding column-wise:
Page No 84:
Question 9:
Subtract:
3a2b from −5a2b
Answer:
On arranging the terms of the given expressions in the descending powers of and subtracting:
Page No 84:
Question 10:
Subtract:
−8pq from 6pq
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 11:
Subtract:
−2abc from −8abc
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 12:
Subtract:
−16p from −11p
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 13:
Subtract:
2a − 5b + 2c − 9 from 3a − 4b − c + 6
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 14:
Subtract:
−6p + q + 3r + 8 from p − 2q − 5r − 8
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 15:
Subtract:
x3 + 3x2 − 5x + 4 from 3x3 − x2 + 2x − 4
Answer:
On arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Page No 84:
Question 16:
Subtract:
5y4 − 3y3 + 2y2 + y − 1 from 4y4 − 2y3 − 6y2 − y + 5
Answer:
Arranging the terms of the given expressions in the descending powers of and subtracting column-wise:
Page No 84:
Question 17:
Subtract:
4p2 + 5q2 − 6r2 + 7 from 3p2 − 4q2 − 5r2 − 6
Answer:
Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:
Page No 84:
Question 18:
What must be subtracted from 3a2 − 6ab − 3b2 − 1 to get 4a2 − 7ab − 4b2 + 1?
Answer:
Let the required number be .
∴ Required number =
Page No 84:
Question 19:
The two adjacent sides of a rectangle are 5x2 − 3y2 and x2 + 2xy. Find the perimeter.
Answer:
Sides of the rectangle are and .
Perimeter of the rectangle is .
Page No 84:
Question 20:
The perimeter of a triangle is 6p2 − 4p + 9 and two of its sides are p2 − 2p + 1 and 3p2 − 5p + 3. Find the third side of the triangle.
Answer:
Let be the three sides of the triangle.
∴ Perimeter of the triangle =
Given perimeter of the triangle =
One side () =
Other side () =
Perimeter =
Thus, the third side is .
Page No 87:
Question 1:
Find the product:
(5x + 7) × (3x + 4)
Answer:
By horizontal method:
Page No 87:
Question 2:
Find the product:
(4x + 9) × (x − 6)
Answer:
By horizontal method:
Page No 87:
Question 3:
Find the product:
(2x + 5) × (4x − 3)
Answer:
By horizontal method:
Page No 87:
Question 4:
Find the product:
(3y − 8) × (5y − 1)
Answer:
By horizontal method:
Page No 87:
Question 5:
Find the product:
(7x + 2y) × (x + 4y)
Answer:
By horizontal method:
Page No 87:
Question 6:
Find the product:
(9x + 5y) × (4x + 3y)
Answer:
By horizontal method:
Page No 87:
Question 7:
Find the product:
(3m − 4n) × (2m − 3n)
Answer:
By horizontal method:
Page No 87:
Question 8:
Find the product:
(x2 − a2) × (x − a)
Answer:
By horizontal method:
i.e
Page No 87:
Question 9:
Find the product:
(x2 − y2) × (x + 2y)
Answer:
By horizontal method:
Page No 87:
Question 10:
Find the product:
(3p2 + q2) × (2p2 − 3q2)
Answer:
By horizontal method:
Page No 87:
Question 11:
Find the product:
(2x2 − 5y2) × (x2 + 3y2)
Answer:
By horizontal method:
Page No 87:
Question 12:
Find the product:
(x3 − y3) × (x2 + y2)
Answer:
By horizontal method:
Page No 87:
Question 13:
Find the product:
(x4 + y4) × (x2 − y2)
Answer:
By horizontal method:
Page No 87:
Question 14:
Find the product:
Answer:
By horizontal method:
Page No 87:
Question 15:
Find the product:
(x2 − 3x + 7) × (2x + 3)
Answer:
By horizontal method:
Page No 87:
Question 16:
Find the product:
(3x2 + 5x − 9) × (3x − 5)
Answer:
By horizontal method:
Page No 87:
Question 17:
Find the product:
(x2 − xy + y2) × (x + y)
Answer:
By horizontal method:
Page No 87:
Question 18:
Find the product:
(x2 + xy + y2) × (x − y)
Answer:
By horizontal method:
Page No 87:
Question 19:
Find the product:
(x3 − 2x2 + 5) × (4x − 1)
Answer:
By horizontal method:
Page No 87:
Question 20:
Find the product:
(9x2 − x + 15) × (x2 − 3)
Answer:
By horizontal method:
Page No 87:
Question 21:
Find the product:
(x2 − 5x + 8) × (x2 + 2)
Answer:
By horizontal method:
Page No 87:
Question 22:
Find the product:
(x3 − 5x2 + 3x + 1) × (x3 − 3)
Answer:
By horizontal method:
Page No 87:
Question 23:
Find the product:
(3x + 2y − 4) × (x − y + 2)
Answer:
By horizontal method:
Page No 87:
Question 24:
Find the product:
(x2 − 5x + 8) × (x2 + 2x − 3)
Answer:
By horizontal method:
Page No 87:
Question 25:
Find the product:
(2x2 + 3x − 7) × (3x2 − 5x + 4)
Answer:
By horizontal method:
Page No 87:
Question 26:
Find the product:
(9x2 − x + 15) × (x2 − x − 1)
Answer:
By horizontal method:
Page No 90:
Question 1:
Divide:
(i) 24x2y3 by 3xy
(ii) 36xyz2 by −9xz
(iii) −72x2y2z by −12xyz
(iv) −56mnp2 by 7mnp
Answer:
(i) 24x2y3 by 3xy
Therefore, the quotient is 8xy2.
(ii) 36xyz2 by −9xz
Therefore, the quotient is −4yz.
(iii)
Therefore, the quotient is 6xy.
(iv) −56mnp2 by 7mnp
Therefore, the quotient is −8p.
Page No 90:
Question 2:
Divide:
(i) 5m3 − 30m2 + 45m by 5m
(ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy
(iii) 9x2y − 6xy + 12xy2 by − 3xy
(iv) 12x4 + 8x3 − 6x2 by − 2x2
Answer:
(i) 5m3 − 30m2 + 45m by 5m
Therefore, the quotient is m2 − 6m + 9.
(ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy
Therefore, the quotient is 4xy − 3y + 5xy2.
(iii) 9x2y − 6xy + 12xy2 by − 3xy
Therefore, the quotient is −3x + 2 − 4y.
(iv) 12x4 + 8x3 − 6x2 by − 2x2
Therefore the quotient is −6x2 − 4x + 3.
Page No 90:
Question 3:
Write the quotient and remainder when we divide:
(x2 − 4x + 4) by (x − 2)
Answer:
Therefore, the quotient is and the remainder is 0.
Page No 90:
Question 4:
Write the quotient and remainder when we divide:
(x2 − 4) by (x + 2)
Answer:
Therefore, the quotient is −2 and the remainder is 0.
Page No 90:
Question 5:
Write the quotient and remainder when we divide:
(x2 + 12x + 35) by (x + 7)
Answer:
(x2 + 12x + 35) by (x + 7)
Therefore, the quotient is and the remainder is 0.
Page No 90:
Question 6:
Write the quotient and remainder when we divide:
(15x2 + x − 6) by (3x + 2)
Answer:
Therefore, the quotient is and the remainder is 0.
Page No 90:
Question 7:
Write the quotient and remainder when we divide:
(14x2 − 53x + 45) by (7x − 9)
Answer:
Therefore, the quotient is and the remainder is 0.
Page No 90:
Question 8:
Write the quotient and remainder when we divide:
(6x2 − 31x + 47) by (2x − 5)
Answer:
Therefore, the quotient is and the remainder is 7.
Page No 90:
Question 9:
Write the quotient and remainder when we divide:
(2x3 + x2 − 5x − 2) by (2x + 3)
Answer:
Therefore, the quotient is and the remainder is 1.
Page No 90:
Question 10:
Write the quotient and remainder when we divide:
(x3 + 1) by (x + 1)
Answer:
Therefore, the quotient is -x+1 and the remainder is 0.
Page No 90:
Question 11:
Write the quotient and remainder when we divide:
(x4 − 2x3 + 2x2 + x + 4) by (x2 + x + 1)
Answer:
Therefore, the quotient is ( x2 - 3x + 4) and remainder is 0.
Page No 90:
Question 12:
Write the quotient and remainder when we divide:
(x3 − 6x2 + 11x − 6) by (x2 − 5x + 6)
Answer:
Therefore, the quotient is (x-1) and the remainder is 0.
Page No 90:
Question 13:
Write the quotient and remainder when we divide:
(5x3 − 12x2 + 12x + 13) by (x2 − 3x + 4)
Answer:
Therefore, the quotient is ( 5x+ 3) and the remainder is (x + 1).
Page No 90:
Question 14:
Write the quotient and remainder when we divide:
(2x3 − 5x2 + 8x − 5) by (2x2 − 3x + 5)
Answer:
Therefore, the quotient is (x-1) and the remainder is 0.
Page No 90:
Question 15:
Write the quotient and remainder when we divide:
(8x4 + 10x3 − 5x2 − 4x + 1) by (2x2 + x − 1)
Answer:
Therefore, the quotient is ( 4x2+ 3x -2) and the remainder is ( x-1).
Page No 93:
Question 1:
Find each of the following products:
(i) (x + 6)(x + 6)
(ii) (4x + 5y)(4x + 5y)
(iii) (7a + 9b)(7a + 9b)
(iv)
(v) (x2 + 7)(x2 + 7)
(vi)
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Page No 93:
Question 2:
Find each of the following products:
(i) (x − 4)(x − 4)
(ii) (2x − 3y)(2x − 3y)
(iii)
(iv)
(v)
(vi)
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
Page No 93:
Question 3:
Expand:
(i) (8a + 3b)2
(ii) (7x + 2y)2
(iii) (5x + 11)2
(iv)
(v)
(vi) (9x − 10)2
(vii) (x2y − yz2)2
(viii)
(ix)
Answer:
We shall use the identities (a+b)2 =a2 +b2 +2ab and (a-b)2 =a2 +b2 -2ab.
(i) We have:
(ii)We have:
(iii) We have :
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Page No 94:
Question 4:
Find each of the following products:
(i) (x + 3)(x − 3)
(ii) (2x + 5)(2x − 5)
(iii) (8 + x)(8 − x)
(iv) (7x + 11y)(7x − 11y)
(v)
(vi)
(vii)
(viii)
Answer:
(i) We have:
(ii) We have:
(iii) We have:
(iv) We have:
(v) We have:
(vi) We have:
(vii) We have:
(viii) We have:
(ix) We have:
Page No 94:
Question 5:
Using the formula for squaring a binomial, evaluate the following:
(i) (54)2
(ii) (82)2
(iii) (103)2
(iv) (704)2
Answer:
We shall use the identity (a+b)2 =a2 +b2 +2ab.
(i)
(ii)
(iii)
(iv)
Page No 94:
Question 6:
Using the formula for squaring a binomial, evaluate the following:
(i) (69)2
(ii) (78)2
(iii) (197)2
(iv) (999)2
Answer:
We shall use the identity (a-b)2 = a2 +b2 -2ab.
(i)
(ii)
(iii)
(iv)
Page No 94:
Question 7:
Find the value of:
(i) (82)2 − (18)2
(ii) (128)2 − (72)2
(iii) 197 × 203
(iv)
(v) (14.7 × 15.3)
(vi) (8.63)2 − (1.37)2
Answer:
We shall use the identity (a-b) (a+b)=a2 - b2.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Page No 94:
Question 8:
Find the value of the expression (9x2 + 24x + 16), when x = 12.
Answer:
Therefore, the value of the expression (9x2 + 24x + 16), when x = 12, is 1600.
Page No 94:
Question 9:
Find the value of the expression (64x2 + 81y2 + 144xy), when x = 11 and
Answer:
Therefore, the value of the expression (64x2 + 81y2 + 144xy), when x = 11 and
Page No 94:
Question 10:
Find the value of the expression (36x2 + 25y2 − 60xy), when and
Answer:
Page No 94:
Question 11:
If , find the values of
(i) and
(ii) .
Answer:
Therefore, the value of x2+ is 14.
Therefore, the value of x4 + is 194.
Page No 94:
Question 12:
If , find the values of
(i)
(ii)
Answer:
Page No 94:
Question 13:
Find the continued product:
(i) (x + 1)(x − 1)(x2 + 1)
(ii) (x − 3)(x + 3)(x2 + 9)
(iii) (3x − 2y)(3x + 2y)(9x2 + 4y2)
(iv) (2p + 3)(2p − 3)(4p2 + 9)
Answer:
Page No 94:
Question 14:
If x + y = 12 and xy = 14, find the value of (x2 + y2).
Answer:
Page No 94:
Question 15:
If x − y = 7 and xy = 9, find the value of (x2 + y2).
Answer:
Page No 94:
Question 1:
Tick (✓) the correct answer:
The sum of (6a + 4b − c + 3), (2b − 3c + 4), (11b − 7a + 2c − 1) and (2c − 5a − 6) is
(a) (4a − 6b + 2)
(b) (−3a + 14b − 3c + 2)
(d) (−6a + 17b)
(d) (−6a + 6b + c −4)
Answer:
(c) (−6a + 17b)
Page No 95:
Question 2:
Tick (✓) the correct answer:
(3q + 7p2 − 2r3 + 4) − (4p2 − 2q + 7r3 − 3) = ?
(a) (p2 + 2q + 5r3 + 1)
(b) (11p2 + q + 5r3 + 1)
(c) (−3p2 − 5q + 9r3 − 7)
(d) (3p2 + 5q − 9r3 +7)
Answer:
(d) (3p2 + 5q − 9r3 +7)
Page No 95:
Question 3:
Tick (✓) the correct answer:
(x + 5)(x − 3) = ?
(a) x2 + 5x − 15
(b) x2 − 3x − 15
(c) x2 + 2x + 15
(d) x2 + 2x − 15
Answer:
(d) x2 + 2x − 15
Page No 95:
Question 4:
Tick (✓) the correct answer:
(2x + 3)(3x − 1) = ?
(a) (6x2 + 8x − 3)
(b) (6x2 + 7x − 3)
(c) 6x2 − 7x − 3
(d) (6x2 − 7x + 3)
Answer:
(b) (6x2 + 7x − 3)
Page No 95:
Question 5:
Tick (✓) the correct answer:
(x + 4)(x + 4) = ?
(a) (x2 + 16)
(b) (x2 + 4x + 16)
(c) (x2 + 8x + 16)
(d) (x2 + 16x)
Answer:
(c) (x2 + 8x + 16)
Page No 95:
Question 6:
Tick (✓) the correct answer:
(x − 6)(x − 6) = ?
(a) (x2 − 36)
(b) (x2 + 36)
(c) (x2 − 6x + 36)
(d) (x2 − 12x + 36)
Answer:
(d) (x2 − 12x + 36)
Page No 95:
Question 7:
Tick (✓) the correct answer:
(2x + 5)(2x − 5) = ?
(a) (4x2 + 25)
(b) (4x2 − 25)
(c) (4x2 − 10x + 25)
(d) (4x2 + 10x − 25)
Answer:
(b) (4x2 − 25)
Page No 95:
Question 8:
Tick (✓) the correct answer:
8a2b3 ÷ (−2ab) = ?
(a) 4ab2
(b) 4a2b
(c) −4ab2
(d) −4a2b
Answer:
(c) −4ab2
Page No 95:
Question 9:
Tick (✓) the correct answer:
(2x2 + 3x + 1) ÷ (x + 1) = ?
(a) (x + 1)
(b) (2x + 1)
(c) (x + 3)
(d) (2x + 3)
Answer:
(b) (2x + 1)
Page No 95:
Question 10:
Tick (✓) the correct answer:
(x2 − 4x + 4) ÷ (x − 2) = ?
(a) (x − 2)
(b) (x + 2)
(c) (2 − x)
(d) (2 + x + x2)
Answer:
(a) (x − 2)
Page No 95:
Question 11:
Tick (✓) the correct answer:
(a + 1)(a − 1)(a2 + 1) = ?
(a) (a4 − 2a2 − 1)
(b) (a4 − a2 − 1)
(c) (a4 − 1)
(d) (a4 + 1)
Answer:
(c) (a4 − 1)
Page No 95:
Question 12:
Tick (✓) the correct answer:
(a)
(b)
(c)
(d)
Answer:
a)
(1x2−1y2)
Page No 95:
Question 13:
Tick (✓) the correct answer:
If , then
(a) 25
(b) 27
(c) 23
(d)
Answer:
(c) 23
Page No 95:
Question 14:
Tick (✓) the correct answer:
If , then
(a) 36
(b) 38
(c) 32
(d)
Answer:
(b) 38
Page No 95:
Question 15:
Tick (✓) the correct answer:
(82)2 − (18)2 = ?
(a) 8218
(b) 6418
(c) 6400
(d) 7204
Answer:
(c) 6400
[using the identity (a-b)(a+b)=a2 -b2]
Page No 95:
Question 16:
Tick (✓) the correct answer:
(197 × 203) = ?
(a) 39991
(b) 39999
(c) 40009
(d) 40001
Answer:
(a) 39991
[using the identity (a+b) (a-b) = a2 -b2]
Page No 95:
Question 17:
Tick (✓) the correct answer:
If (a + b) = 12 and ab = 14, then (a2 + b2) = ?
(a) 172
(b) 116
(c) 165
(d) 126
Answer:
(b) 116
Page No 95:
Question 18:
Tick (✓) the correct answer:
If (a − b) = 7 and ab = 9, then (a2 + b2) = ?
(a) 67
(b) 31
(c) 40
(d) 58
Answer:
(a) 67
Page No 95:
Question 19:
Tick (✓) the correct answer:
If x = 10, then the value of (4x2 + 20x + 25) = ?
(a) 256
(b) 425
(c) 625
(d) 575
Answer:
(c) 625
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