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Frank ICSE Mathematics Class 8 Solutions Chapter 10 Algebraic Expressions
Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Frank ICSE Mathematics Class 8 Math Book, Chapter 10, Algebraic Expressions. Here students can easily find step by step solutions of all the problems for Algebraic Expressions, Exercise 10.1, 10.2, 10.3 and 10.4 Also our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 10 solutions. Here in this post all the solutions are based on latest Syllabus.
Algebraic Expressions Exercise 10.1 Solution :
Question no – (1)
Solution :
(a) 4x + 8
Terms = 4x
Coefficients = 4
Constants = 8
(b) 7a2 – a + 16
Terms = 7a2
Coefficients = 7
Constants = 16
(c) 17ab + 11bc – 3cd
Terms = 17ab 11bc – 3cd
Coefficients = 17 1 – 3
Constants = 0
(d) 0.75pq + 0.25p – 0.32
Terms = 0.75pq 0.25p
Coefficients = 0.75 0.25
Constants = – 0.32
(e) m/2 – n/2 + 5
Terms = m/2 – n/3
Coefficients = 1/2 – 1/3
Constants = 0
(f) 9x2 + 7y2 + 12z2
Terms = 9x2 7y2 12z2
Coefficients = 9 7 12
Constants = 0
Question no – (2)
Solution :
(a) Binomial
(b) Monomial
(c) Trinomial
(d) Binomial
(e) Monomial
(f) Binomial
(g) Trinomial
(h) Trinomial
Question no – (3)
Solution :
= 14xy, – 6yx; 7x2y, 21yx2; 12abc – 17bac; 17xy2, 4xy2; – n2m2, 8m2n2; 18pqr, 15pqr; 18p2qr, 7rqp2
Question no – (4)
Solution :
(a) 6x + 4y – 3z
7x – 11y – 9z
14x + 8y – 6z
—————————————
27x + y – 182
(b) 7p – 8q + 11r + 13
10p – 13p + 18
8p – 5q – 14r + 12
5p + 17q + 14r
—————————————
30p – 9q + 11r + 43
(c) 8x2 + 7x 12
17x2 – 15x – 21
– 9x2 + 11x + 4
4x2 – 18x + 19
—————————————
20x2 – 18x + 14
(d) 6ax – 2by + 3cz
– 11ax + 16by – 15cz
– 9ax – 3by + 10cz
—————————————
– 14ax + 11by – 2cz
(e) 15m2n – 17mn + 8mn2
13m2n – 15mn – 9mn2
12m2n + 21mn – 14mn2
—————————————
40m2n – 1mn – 15mn2
(f) 13x + 17y – 19z + 2
14x + 12y – 31
– 15x + 6z + 12
2x + y + 11z + 9
—————————————
14x + 30y – 2z – 8
Question no – (5)
Solution :
(a) 17x + 8y – 15z
+ 12x + 7y – 15z
—————————————
5x + y + 0
(b) 12ax + 6by + 111cz
+ 21ax + 15by – 6cz
—————————————
-9ax – 9by + 17cz
(c) 16x3 + 14x2 – 9x + 15
+ 17x3 – 19x2 – 21
—————————————–
x3 + 33×2 – 22x + 36
(d) 7p + 11q – 2r + 9
– 8p – 4q + 6r + 15
—————————————
15p + 15q + 8r – 6
Question no – (6)
Solution :
= [(13 + 19b + 12c) + (14a + 21b + 11c)]
= [(17a + 13b – 15c) + (8a + 12b – 18c)]
= [(13a + 14a) + 19b) + (12c + 11c)]
= [17a + 8a) + (13b + 126) + (- 15c – 18c)]
= [27a – 2b + 23c] – [25a + 25b – 33c]
= (27a – 25a) + (- 2b + 256) + (23c – 33c)
= 2a + 23b – 10c
Question no – (7)
Solution :
(a) A + B + C
= (5x + 11y + 152) + (12x – 13y + 152) + (12x – 13y + 19z) + (7x – 6y 21z)
= (5x + 12 + 7x) + 911y – 13y – 6y) + (15z + 19z + 21z)
= 24x – 7y + 25z
(b) A – B – C
= (5x + 11y – 15z) – (12x – 13y + 192) – (7x – 6y + 21z)
= (5x – 12x – 7x) + (11y + 13y + 6y) + (15z – 19z – 21z)
= – 14x + 30y – 55z
(c) A + B – C
= (5x + 11y – 15z) + (12x – 13y + 19z) – (7x – 6y + 21z)
= (5x – 12x – 7x) + (11y – 13y + 6y) + (- 15z + 19z – 121z)
= – 14x + 4y – 17z
(d) 2A + 3B + C
= 2(5x + 11y – 15z) + 3 (12x – 13y + 19z) + (7x – 6y + 21z)
= (10x + 22y – 20z) + (36x – 39y + 57z) + (7x – 6y + 21z)
= (10x + 36x + 7x) + (22y – 39y – 6y) + (- 30z + 57z + 21z)
= 910x + 36x + 7x) + (22y – 39y – 6y) + (- 30z + 57z + 21z)
= 53x – 23y + 48z
Question no – (8)
Solution :
As we know that,
Other side = 1/2 (Perimeter) – (given side)
Now,
= 1/2 (16a + 8b – 6c) – (5a + 3b – 4c)
= (8a + 4b – 3c) – (5a + 3b – 4c)
= (8a – 5a) + (4b – 3b) – (3c + 4c)
= 3a + b – 7c
Therefore, the other side will be 3a + b – 7c
Question no – (9)
Solution :
As we know that,
Third side = [Perimeter – (sum of 2 other side)
Now,
= (18p + 12q + 13r) – (5p + 3q – 4r) + (6p + 5q + 7r)
= (18p + 12q + 13r) – [11 + 8q + 3r]
= (18p – 11p) + (12q – 8q) + (13r – 3r)
= 7p + 4q + 10r
Therefore, the third side will be 7p + 4q + 10r
Algebraic Expressions Exercise 10.2 Solution :
Question no – (1)
Solution :
(a) (m + 3)n
= m. m + 3.m
= m2 + 3m
(b) 5(3x – 2)
= 5.x – 5.2
= 5x – 10
(c) 8(2x – 3y)
= 8.2x – 8.3y
= 16x – 24y
(d) 3x (x + y)
= 3x.x + 3x.y
= 3x2 + 3xy
(e) 2x (12x – 11y)
= 2x (12x – 1y)
= 2x.12x – 2x.11y
= 24x2 – 22xy
(f) x(3 – 2x + 5y)
= x.3 – x.2 + x.5y
= 3x – 2x2 + 5xy
(g) 15x (x + 5) + 7
= 15x.x + `5x.5 + 7
= 15×2 + 75n + 7
(h) 12x (x + 3y + 8z)
= 12x.x + 12x.3y + 12x.8z
= 12×2 + 36y + 96xz
(i) 10a(a – 5b + 3c)
= 10a.a – 10a.5b + 10a.3c
= 10a2 – 50ab + 30ac
(j) 6x (x + 3y + 5z)
= 6x.x + 6x.3y+ 6x.5z
= 6x2 + 18xy + 30xz
(k) 4x (x2 + 3x + 9)
= 4x.x2 + 4x.3x + 4x.9
= 4x3 + 12×2 + 36x
Question no – (2)
Solution :
(a) 3 + 2(x + 1)
= 3 + 2x + 2
= 2x + 3 + 2
= 2x + 5
(b) 7(x + 1) + 4(x + 3)
= 7x + 7 + 4x + 12
= 7x + 4x + 7 + 12
= 11x + 19
(c) 3(x – 8) + 5(2x – 3)
= 3x – 24 + 10x – 15
= 3x + 10x – 24 – 15
= 13x – 39
(d) 4(x + 11) + 13(2 + x)
= 4x + 44 + 26 + 13x
= 17x + 70
(e) 12(x – 6) + (x + 7)y
= 12x – 12 + xy + 7y
(f) x(x + 3) + x(3x + 1)
= x2 + 3x + 3x2 + x
= (x2 + 3x2) + (3x + x)
= 4x2 + 4x
(g) 10x(x + 5) – 2
= 10x2 + 50x – 2
(h) x(x + 8y) + 5x(x + y)
= x2 + 8xy + 5x2 + 5xy
= 5x2 + x2 + 8xy + 5xy
= 6x2 + 13xy
(i) 4(a + 10b) + 3(a + b)
= 4a + 10b + 3a + 3b
= 4a + 3a + 10b + 3b
= 7a + 13b
Question no – (3)
Solution :
(a) (5a + 11b) (8a + 9b)
= (5a. 8a) + (5a, 9b) + (11b.8a) + (11b.9b)
= 40a2 + 45ab + 88ab + 99b2
= 40a2 + 133ab + 99b2
(b) (11p – 9p) (4p + 17p)
= (110.4p) – (9q .4p) + (11p.17q – (9q .17q)
= 44p2 – 36pq + 187pq – 153q2
= 44p2 + 151pq – 153q2
(c) (7x2 + 4y2) (3x2 + 8y2)
= (7x2. 3x2) + (7x2. 8y2) + (4y2.3x2) + (4y2.8y2)
= 21x4 + 56x2y2 + 12x2y2 + 32y4
= 21x4 + 68x2y2 + 32x4
(d) (13xy – 3z) (15xy – 8z)
= (13xy.15xy) – (3z.15xy) – (13xy.8z) + (3z, 8z)
= 195x2y2 – 45xyz – 104xyz + 24x2
= 195x2y2 – 149xyz + 25z2
Question no – (4)
Solution :
(a) (6a + 8b – 11) (3a + 7b)
6a + 8b – 11
3a + 7b
————————————————-
18a2 + 24ab – 33a
+ 421b + 56b2 – 77b
————————————————-
18a2 + 66ab – 33a + 56b2 – 77b
∴ The product will be 18a2 + 66ab – 33a + 56b2 – 77b
(b) (3x2 + 7x – 6) (4x + 11)
3x2 + 7x – 6
4x + 11
————————————————-
12x3 28x2 – 24x
33x2 + 77x – 66
————————————————-
12x3 + 6 1 x2 + 53x – 66
(c) (7p2 – 13pq + 6q2)
7p2 – 13pq + 6q2
5p – 79
————————————————-
35p3 – 65p2q + 30pq2
– 49p2q + 91pq2 – 42q3
————————————————-
35p3 – 114p2q + 121p2q – 42q3
(d) (3m2 + 7mn + 9n2) (4m – 5n)
= 3m2 + 7mn +9n2
4m – 5n
————————————————-
13m3 + 28m2n + 36mn2
– 15m2n – 35mn2 – 45n2
————————————————-
12m3+ 13m2n +mn2 – 45x3
(f) (3m2 + 7mn + 9n2) (4m – 5n)
3m2 + 7mn +9n2
4m – 5n
————————————————-
13m3 + 28m2n + 36mn2
– 15m2n – 35mn2 – 45n2
————————————————-
12m3+ 13m2n +mn2 – 45x3
Algebraic Expressions Exercise 10.3 Solution :
Question no – (1)
Solution :
(a) 16x2 + 72xy + 81y2
(b) 9a2 + 48ab + 64b2
(c) 9x2 + 24xy + 16y2
(d) 4p2 + 60pq +225q2
(e) 25x2 + 81y2 + 90xy
(f) 9p2 + 42pq + 49q2
(g) x2y2 + 4xy + 4
(h) 121x2 + 110x + 25
(i) 64m2 + 80m + 4
(j) 49a2/9 + 2ab + 9b2/49
(k) 25a2b2 + 70ab + 49
(l) 3 + 2√2
Question no – (2)
Solution :
(a) a2 – 6a + 9
(b) 4x2 – 20x + 25
(c) 25a2 -60ab + 36b2
(d) a2b2 – 2abcd+ c2d2
(e) 9m2/4 – 2mn + 4n2/9
(f) 36a2b2 – 84abc + 49c2
(g) 16x2 – 24xy + 9y2
(h) 9x2 + 1/9x2 – 2
Question no – (3)
Solution :
(a) 24ab
(b) 80ab
(c) 180xy
(d) 420ab
Question no – (4)
Solution :
(a) a2 – 4
(b) x2 – 49
(c) x2 – 9
(d) 64x2 – 25y2
(e) 16xy – y2
(f) p2 – 4q2
(g) 9x2 – 16
(h) 49x2 – 16/y2
Question no – (5)
Solution :
(i) – (a) (104)2
= (100 + 4)2
= (100)2 + 2.100.4 + (4)2
= 10000 + 800 + 16
= 10816
(i) – (b) (103)2
= (100 + 3)2
= (100)2 + 2.100.3 + (3)2
= 10000 + 600 + 9
= 10609
(i) – (c) (54)2
= (50 + 4)2
= (50)2 + 2.504 + (4)2
= 2500 + 400 + 16
= 2916
(i) – (d) (52)2
= (50 + 2)2
= (50)2 + 2.50.2 + (2)2
= 2500 + 200 + 4
= 2704
(i) – (e) (10.1)2
= (10 + 01)2
= (10)2 + 2.10 (0.1) + (0.1)2
= 100 + 2 + 001
= 102021
(i) – (f) (10.2)2
= (10 + 0.2)2
= (10)2 + 2.10. (0.2)2
= 100 + 4 + 0.04
= 104.04
(ii) – (a) (97)2
= (100 – 3)2
= (100)2 – 2.100.(3) + (3)2
= 10000 – 600 + 9
= 9409
(ii) – (b) (98)2
= (100 – 2)2
= (100)2 + (2)2
= 10000 – 400 + 4
= 9604
(ii) – (c) (49)2
= (50 – 1)2
= (50)2 – 2.50.1 + (1)2
= 2500 – 100 + 1
= 2401
(ii) – (d) (48)2
= (50 – 2)2
= (50)2 – 2.50.2 + (2)2
= 2500 – 200 + 4
= 2304
(ii) – (e) (9.9)2
= (10 – 0.1)2
= (10)2 – 2.(10) (0.1) + (0.1)2
= 100 – 2 + 0.01
= 98.01
(ii) – (f) (9.8)2
= (10 – 0.2)2
= (10)2 – 2 (10) (0.2)2 + (0.2)
= 100 – 4 + 0.04
= 96.04
(iii) – (a) 59 × 61
= (60 – 1) (60 + 1)
= (60)2 – (1)2
= 3600 – 1
= 3599
(iii) – (b) 102 × 98
= (100 + 2) (100 – 2)
= (100)2 – (2)2
= 10000 – 4
= 9996
(iii) – (c) 48 × 52
= (50 – 2) (50 + 2)
= (50)2 – (2)2
= 2500 – 4
= 2496
(iii) – (d) 103 × 97
= (100 + 3) (100 – 3)
= (100)2 – (3)2
= 10000 – 9
= 9991
(iii) – (e) 49 × 51
= (50 – 1) (50 + 1)
= (50)2 – (1)2
= 2500 – 1
= 2499
(iii) – (f) 612 – 602
= (61 + 60)
= (61 + – 60)
= (121) (10
= 121
(iii) – (g) 732 – 722
= (73 + 72) (73 – 72)
= 145 × 1
= 45
(iii) – (h) 762 – 242
= (76 + 24)
= (76 – 24)
= 100 × 48
= 4800
(iii) – (i) 572 – 432
= (57 + 43) (57 – 43)
= 100 × 14
= 1400
Question no – (6)
Solution :
In the question we get,
(x + y) = 13
xy = 22
Now, x2 + y2
= (x + y)2 – 2xy
= (13)2 – 2.22
= 169 – 44
= 125
Therefor, The value of x2 + y2 will be 125
Question no – (7)
Solution :
In the question we get,
(x – y) = 5
xy = 36
Now, (x – y)2 + 2xy
= (5)2 + 2.36
= 25 + 72
= 97
Question no – (8)
Solution :
From the question we get,
(x2 + y2) = 74
xy = 35
Now, (a) x + y
= (x + y)2 = x2 + y2 + 2xy
= or, (x + y)2 = 74 + 2.35
or, (x + y)2 = 74 + 70
or, (x + y)2 = 144
or, (x + y) = √144
or, (x + y) = 12
Therefore, The value of x + y will be 12
(b) x – y
= (x – y)2 = x2 + y2 – 2xy
or, (x – y)2 = 74 – 2.35
or,(x – y)2 = 74 – 70
or, (x – y)2 = 4
or, (x – y) = √4
or, (x – y) = 2
Therefore, The value of x – y will be 2
Question no – (9)
Solution :
In the question we get,
(2x + 3y) = 14
xy = 8
Now, (2x)2 + 93y)2
= (2x + 3y)2 – 2 (2x) (3y)
= (14)2 – 12xy = (14)2 – 12(8)
= 196 – 96
= 100
Therefor, The value of 4x2 + 9y2 will be 100.
Question no – (10)
Solution :
In the question we get,
(x + y) = 15
xy = 54
Now, (x – y) = √(x +y)2 – 4xy
= √(15)2 – 4.54
= √225 – 216
= √9 = 3
= (x2 – y2)
= (x + y) (x – y)
= 15 × 3
= 45
Question no – (11)
Solution :
In the question we get,
x + 1/x = 5
(a) x2 + 1/x2
= (x + 1/x)2 – 2.x 1/x
= (52)2 – 2 = 25 – 2
= 23
Therefor, The value of x2 + 1/x2 will be 23
(b) x4 + 1/x4
= (x2 + 1/x) – 2.x2 – 1/x
= (23)2 – 2
= 529 – 2
= 527
Therefore, the value of x4 + 1/x4 will be 527
Question no – (12)
Solution :
In the question we get,
x + 1/x = √3
(a) x2 + 1/x2
= (x + 1/x)2 – 2x 1/x
= (√3)2 – 2
= 3 – 2
= 1
Therefore, the value of x2 + 1/x2 will be 1
(b) x4 + 1/x4
= (x2 + 1/x) – 2.x2 – 1/x2
= (1)2 – 2
= 1 – 2
= – 1
Hence, the value of x4 + 1/x4 will be – 1
Question no – (13)
Solution :
(a) If x2 + 1/x2 = 62
Now, x2 + 1/x = 62
or, (x + 1/x)2 – 2. x. 1/x = 62
or, (x + 1/x)2 – 2 = 62
or, (x + 1/x)2 = 64
or, x + 1/x
= √64
= 8
Thus, the value of x2 + 1/x will be 8
(b) x2 + 1/x2 = 79
= x2 + 1/x2 = 79
= (x + 1/x)2 – 2.x. 1/x = 79
or, (x + 1/x)2 – 2 = 79
or, (x + 1/x) = 81
∴ (x + 1/x)
= √81
= 9
Hence, the value of x2 + 1/x2 will be 9
Question no – (14)
Solution :
(a) x2 + 1/x2 = 102
Now, x2 + 1/x2 = 102
or, (x – 1/x)2 + 2.x = 1/x = 102
or, (x – 1/x)2 = 100
or (x – 1/x)
= √10
Therefore, The value of x2 + 1/x2 will be √10
(b) x2 + 1/m2 = 38
Now, x2 + 1/m2 = 38
or, (x – 1x)2 + 2.x /x = 38
or, (x – 1/x) = 36
or, (x – 1/x)
= √36
= 6
Therefor, The value of x2 + 1/m2 will be 6
Question no – (15)
Solution :
In the question we get,
9x2 + y2 = 397
xy = 38
Now, = (3x + y)
= √9x2 + y2 + 2xy
= √397 + 2.38
= √397 + 76
= √473
Therefore, the value of 9x2 + y2 will be √473
Algebraic Expressions Exercise 10.4 Solution :
Question no – (1)
Solution :
(a) 48x3y3z3 by 4x2y2z2
= (4x2y2) (12xyz)/(4x2y2z2)
= 12xyz2
(b) – 81a4b5c7 by a3b2c2
= (27a3b2c2) (- 3ab3c5)/(27a3b2c2)
= – 3ab3c5
(c) 72a3b3c3 by 24a2bc2
= (24a2bc2) (3ab2c)/(24a2bc2)
= 3ab2c
(d) 28x2y2x2 by – 4xyz2
= (- 4xyz2) (- 7xy)/(- 4myz2)
= – 7xy
(e) 55a8b8 by 11a5b5
= (11a5b5) (5a3b3)/(11a5b5)
= 5a3b3
(f) 24a3b3 – 18a2b2 + 12ab by – 6ab
= (- 6ab) (- 4a2b2 + 3ab – 2)/(- 6ab)
= – 4a2b2 + 3ab – 2
Question no – (2)
Solution :
(a) y2 + 5y – 36 by y + 9
(b) x2 + 14x + 48 by x + 6
(c) 5×2 + 31x – 28 by 5x – 4
(d) 3×2 + 10x + 3 by 3x + 1
(e) x2 – 8x – 33 by x + 3
(f) 6×2 – 31x + 40 by 2x – 5
(g) x2 + 2x – 35 by x + 7
(h) 15×2 + x – 6 by 3x + 2
(i) 4a2 – 24a2 + 64a – 128 by a – 4
Question no – (3)
Solution :
(a) 3×2 + 5×2 – 8x – 28 by x – 2
(b) 4×3 + 6×2 – 8x – 5 by 2x + 1
(c) 2×3 + 5×2 – 11 – 14 by 2x + 7
(d) 6×3 + 5×2 – 3x – 2 by 3x – 2
(e) 6×3 + 19×2 + 11x – 6 by 3x – 1
(f) 2×3 – 7×2 – 8x – 3 by 2x – 3
Revision Exercise Questions Solution :
Question no – (1)
Solution :
= [(14a + 9b – 8c) + (12b + 13c – 15a)] – [(8a – 17b + 4c) + (11a – 16b + 17c)]
= [(14a + 15a) + (b + 12b) + (8c + 13c)] – [(8a + 11a) + (- 17b – 16b) + (4c + 17c)]
= [- a + 21b + 5c] – [19a – 33b + 21c]
= (- a – 19a) + (12b + 33b) + (5c + 21c)
= – 2a + 45b – 16c
Question no – (2)
Solution :
8y3 + 7y2 + 3y
3y – 4
——————————————-
24y4 + 21y3 + 9y2
– 32y3 – 28y2 – 12y
——————————————-
24y4 – 11y3 – 19y2 – 12y
Question no – (3)
Solution :
(a) (503)2
= (503)2 = (500 + 3)2
= (500)2 + 2.500.3 + (3)2
= 250000 + 3000 + 9
= 253009
(b) (8.7)2 – (1.3)2
= (87 + 1.3) (87 – 1.3)
= 10 × 7.4
= 74
Question no – (4)
Solution :
(a) (2x + 3y/4)2
= (2x)2 + 2.2x. 3y/4 + (3y/4)2
= 4x2 + 3xy + 9y2/16
(b) (4x2 + 5y2) (4x2 – 5y2)
= (4x2)2 – 5y)2
= 16x4 – 25y4
(c) (x + 2/5) (x – 2/5)
= x2 – (2/5)2
= x2 – 4/25
(d) (xy – 2z)2
= (xy)2 – 2.x.y (+ 2z) + (2z)2
= x2y2 – 4xy2 +4z2
(e) (a + bc) (a – bc) (a2 + b2c2)
= (a2 – b2c2) (a2 + b2c2)
= (a2)2 – (b2c2)
= a4 – b4c4
(f) (2a/3b – 3b/2a)2
= (2a/3b)2 – 2 2a/3b 3b/2a
= 4a2/9b2 – 2 + 9b2/4a2
(g) (- 3a – 4b)2
= [(- 3a + 4b)]2 – (3a + 4b)
= (3a)2 + 3a.4b + (4b)2
= 9a2 + 24ab + 16b2
(h) (a – 7) (a + 7)
= a2 – (7)2
= a2 – 49
Question no – (5)
Solution :
= 104 × 96
= (100 + 4) (100 – 4)
= (100)2 – (4)2
= 10000 – 16
= 9984
Therefore, The value of 104 × 96 will be 9984.
Next Chapter Solution :
👉 Chapter 11 👈
