# Brilliant’s Composite Mathematics Class 7 Solutions Chapter 5

## Brilliant’s Composite Mathematics Class 7 Solutions Chapter 5 Algebraic Expressions

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Brilliant’s Composite Mathematics Class 7 Math Book, Chapter 5, Algebraic Expressions. Here students can easily find step by step solutions of all the problems for Algebraic Expressions, Exercise 5.1, 5.2, 5.3 and 5.4 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.

Algebraic Expressions Exercise 5.1 Solution

Question no – (1)

Solution :

Given, (6 a2bc) × (2 a2b3) × (-5/3 c2)

= 6 × 2 × 5/3 a2 × b4 × c2

= 20a4b4c4

Therefore, the product will be 20a4b4c4

Question no – (2)

Solution :

Given, (4/3pq) × (3/8 p2 r)

= 4/3×3/8 ×p3q

= 1/2 p3qr

Hence, the product will be 1/2 p3qr

Question no – (3)

Solution :

Given, (-3 x2y) × (-4xy2)

= 12x3y3

Thus, the product is 12x3y3

Question no – (4)

Solution :

Given, (-8y3) × (25y2)

= 200y5

Thus, the product is 200y5

Question no – (5)

Solution :

Given, (-7 x2 yz2) × (3/5 x3 y2z)

= -7×3/5×x5y4z4

= -21/5x5y4z4

Question no – (6)

Solution :

Given, (-3/4 pq2r) × (8/5 p2q r3)

= -3/4 × 8/5 p3q3r4

= – 6/5 p3q3r4

Question no – (7)

Solution :

Given, (3a b2) × (4 a2 bc2) × (-3/4 ab3c4)

= 3×4 ×-3/4×a4×b6×c6

= -9a4b6c6

Question no – (8)

Solution :

Given, (5 a5) × (-8a2b4) × (-2a2b3)

= 8a.a9b7

Question no – (9)

Solution :

Given, (8x6y2) × (-20xy)

= -160x7y3

= – 160 × (1)7 ×(2)3

= -320

= [ x = 1, y = 2]

Question no – (10)

Solution :

Given, (5x3) × (-8 xy2) × (-21x2y3)

= -840x6y5

= -840 (1)6 (2)5

= 26240

[x=1 y=2]

Question no – (11)

Solution :

Given, (4.8 x3y6) × (2.5 x4y3)

= 12x7y9

= 12(1)7 (2)9

= 6144

[ x = 1,y = 2]

Question no – (12)

Solution :

Given, (-7/10) × (3/5xy) (-6/15 x2y2)

-7/10 × 3/5 × -6/15

= 21/125 x3y3

= 21/125 ×13×23

= 168/125

[ x = 1, y = 1]

Question no – (13)

Solution :

Given, (5x4) × (-12 xy2) × (-1.5 xy2) × (-1.5 x2y3)

= 90x7y5

= 90 × (1)7(2)5

= 2880

[ x = 1, y = 2]

Question no – (14)

Solution :

Given, (-8/9xy2)×(-18/4x3y4)×(2/5x2y)

= -8/9×-18/4×2/5

= 8/58 x6y7

= 8/5(1)6 (2)7

= 1024/5

Question no – (15)

Solution :

Given, xy2 × (-y2z) × (-x3y2) (3xyz)

= 3x5y2z4

Question no – (16)

Solution :

Given, (-4/7a2b3) × (-2/3 b3c4) × (-7/6 c3a4)

= -4×-2×-7/7×3×6 a6b6c7

= -4/9 a6b6c7

Question no – (17)

Solution :

Given, (-3 x3y) × (16/5 xy2z) × (-15x2y3z3) × (4/15z2)

= -3×16×-15×4/5×15x6y5z6

= 192/5x6y5z6

Question no – (18)

Solution :

Given, (12/25ab)×(5/12bc)×(14/15ca)

12×5×14/15×21×15 a2b2c2

= 8/45 a2b2c2

Algebraic Expressions Exercise 5.2 Solution

Question no – (1)

Solution :

Given, 5x (3x +7)

= 15x2 + 35x

Thus, the product is 15x2 + 35x

Question no – (2)

Solution :

Given, 11x (2x2 y + 5y)

= 22x3 + 55xyz

Hence, the product is 2x3 + 55xyz

Question no – (3)

Solution :

Given, a2 (2x – 5y)

= 2a2x – 5a2y

Thus, the product is 2a2x – 5a2y

Question no – (4)

Solution :

Given, 5/6 x2 (ax3 – by3)

= 5ax3/6 – bx2y3/6

Therefore, the product is 5/6 ax3 – 5/6 bx2y3

Question no – (5)

Solution :

Given, 2x2 (3x -4y2)

= 6x3 – 8y4

Hence, the product is 6x3 – 8y4

Question no – (6)

Solution :

Give, (5x -3) (4xy + 2)

= 20x2y + 10x+12xy – 6

Thus, the product is 20x2y + 10x+12xy – 6

Question no – (7)

Solution :

Given, (2/5 x + 3/2y) [10x – 6y]

= 4x2 – 12xy/5 + 15x – 9y2

Therefore, the product is 4x2 – 12xy/5 + 15x – 9y2

Question no – (8)

Solution :

Given, (2x – 3x) (5x + 7)

= 10x+ 14x – 15x – 21

= 10x2 – x – 21

Thus, the product is 10x2 – x – 21

Question no – (9)

Solution :

Given, (3a2 + 2b2) (2a2 + 3b2)

= 6a4 + 9a2b2 + 4a2b2 + 6a4

= 6a4 + 13a2b2+6b4

Hence, the product is 6a4 + 13a2b2+6b4

Question no – (10)

Solution :

Given, (2/5 x + y) (2/5x – y)

= 4/25 x2 – y2

Therefore, the product is 4/25 x2 – y2

Question no – (11)

Solution :

Given, (x2 + y2) (x2 – y2)

= (x2 + y2) (x2 – y2)

= (x2)2 – (x2)2

= x4 – y4

Question no – (12)

Solution :

Given, (2p + 3p) (2p – 3r)

= (2p + 3p) (2p – 3r)

= 4 pq + 6pr + 312 – 9qr

= 4pq – 3pr + 3q2

Question no – (13)

Solution :

Given, (2m + mn) (3mn – 2m)

= (2m + mn) (3mn – 2m)

= 6m2n – 6m2 + 3m2n2 – 2m2n

= 4m2n – 6m2 + 3m2n2

Question no – (14)

Solution :

Given, (2x – 1) (3x2 – 15x + 7)

= (2x – 1) (3x2 – 15x + 7)

= 6x2 – 30x2 + 14x – 3x2 + 15x – 7

= -33x2 + 29k – 7

Question no – (15)

Solution :

Given, (x2 – 3) (x2 + y2)

= (x2 – 3) (x2 + y2)

= x4 + y2x2 – 3×2 – 3y2

Question no – (16)

Solution :

Given, (x – y) (x2 + xy + y2)

= (x – y) (x2 + xy + y2)

= x3 + x2y + xy2 – x2y – xy2 – y3

= x3 – y3

Question no – (17)

Solution :

Given, (2x + 3y) (4x2 – 6xy + 9y2)

= (2x + 3y) (4x2 – 6xy + 9y2)

= 8x3 – 12x2y + 18xy2 + 12x2y – 18xy2 + 27y3

= 8x3 + 27y3

Question no – (18)

Solution :

Given, (3x + 5) (3x – 8) (6 – 5x)

= (3x + 5) (3x – 8) (6 – 5x)

= (9x2 – 27x + 15x – 40) (6 – 5x)

= (9x2 – 27x + 15x – 40) (6 – 5x)

= (6-5x) (9x2 – 12x – 40)

= 54x2 – 72x – 240 – 54×3 + 60x2 + 200x

= -54x3 + 114x2 + 128 – 240

Question no – (19)

Solution :

Given, (2x – 3) (3x + 5) (5x – 9)

= (2x – 3) (3x + 5) (5x – 9)

= (6x2 + 10x – 9x – 15) (5x – 9)

= (5x -9) (6x2 + x – 15)

= 30x3 + 5x2 – 75x – 54x2 – 9x + 135

= 30x3 + 49x2 – 64x + 135

Question no – (20)

Solution :

Given, (2x + 5) (2x – 7) (2x + 11)

= (2x + 5) (2x – 7) (2x + 11)

= (4x2 – 14x + 10x – 35) (2x + 11)

= (2x + 11) (4x2 – 4x – 35)

= 8x3 – 6x2 – 70x + 44x2 – 44x – 285

= 8x3 + 36x2 – 114x – 385

Question no – (21)

Solution :

Given, (a + bx) (a + cx) (b + zx)

= (a + bx) (a + cx) (b + zx)

= (a2 + cx + abx + bcx) (b + ax)

= (b + ax) (a2 + cx + abx + bcx)

= a2b + bcx + ab2x + b2cx + a3x + acx2 + a2bx2 + abcx

Question no – (22)

Solution :

Given, (2x – 3) (x2 – 3x + 2) – (x – 2) (x+ 4x – 3)

= (2x3 – 6x2 + 4x – 3x2 + 9x – 6) (x3 – 4x2 – 3x – 2x2 + 8x + 6)

= (2x3 – 9x2 + 13x – 6) – (x3 – 6x2 + 5x + 6)

= 2x3 – 9x2 + 13x – 6 – x3 + 6x2 – 5x + 6

= x3 – 3x2 + 8x – 12…(Simplified)

Question no – (23)

Solution :

Given, (4p + 3p) (p – q) – (3p + 4q) (2p – 3q)

= (4p– 4pq – 3pq – 3q2) – (6p2 – 9pq + 8pq + 8pq – 12q2)

= 4p– 3q2 – 6p2 + pq + 12q2

= – 2p2 + 15q…(Simplified)

Question no – (24)

Solution :

(12x3 – 14x2y + 10xy2 – 11x2y + 35xy2 – 25y3

= 12x3 – 25x2y + 45xy2 – 25y3

= (12 × 33) – (25 × 3 × 2) + (45 × 3 × 22) + (25 × 23) [∴ x = 3, y = 2]

= 324 – 150 – 540 + 200

= – 166…(Simplified)

Question no – (25)

Solution :

= 6x4 – 4x3y + 22x2y2 + 3x2y – 2xy2 + 11y3

= (6 × 14) – (4 × 13 × 2) + (22 × 12 × 22) + (3 × 12 × 2) – (2 × 1 × 22) + (11 × 23)

= 6 – 8 + 88 + 6 – 8 + 88

= 172…(Simplified)

Algebraic Expressions Exercise 5.3 Solution

Question no – (1)

Solution :

Given, (2x + 3y) (2x + 3y)

= (2x + 3y)

= (2x2) + 2.2x. 3y + (3y)2

= 4x+ 12xy + 9y

Question no – (2)

Solution :

Given, (3a + 4b) (3a + 4b)

= (3a + 4b)2

= (3a)2 + 2.3a. 4b + (4b)2

= 9a2 + 24ab + 6b

Question no – (3)

Solution :

Given, (3/2 x + 4/3y) (3/2x + 4/3y)

= (3/2x + 4/3y)2

= (3/2x)2 + 2. 3/2x 4/3y + (4/3y)2

= 9x2/4+ 4xy + 16y2/9

Question no – (4)

Solution :

Given, (2p + 5q) (2p + 5q)

= (2p + 5q)2

= (2p)2 + 2.p 5q + (5q)2

= 4p2 + 20pa + 25q

Question no – (5)

Solution :

Given, (2/5x2 – 5/2y2) (2/5x2 – 5/2y2)

= (2/5x2 – 5/2y2)2

= (2/5x2)2 + 2. 2/5x2. 5/2y2 + (5/2y2)2

= 4x4/25 + 2x2y+ 25/4y

Question no – (6)

Solution :

Given, (3/4a – 2/5b) (3/4 a – 2/5b)

= (3/4 a – 2/5b)2

= (3/4a)2 – 2. 3/4a. 2/5b + (2/5b)2

= 9/16 a– 3/5 ab + 4/25 b

Question no – (7)

Solution :

Given, (2x – 7y) (2x – 7y)

= (2x – 7y)2

= (2x)2 – 2.2x.7y + (7y)2

= 4x2 – 28xy + 49y

Question no – (8)

Solution :

Given, (6x2 – 5y2) (6x2 – 5y2)

= (6x2 – 5y2)2

= (6x2)2 + 2.6x2. 5y2 + (5y2)2

= 36x4 + 60x2y2 + (25y4)

Question no – (9)

Solution :

Given, (2p + 3p) (2p – 3q)

= (2p + 3p) (2p – 3q)

= (2p)– (3a)2

= 4p2 – 9q

Question no – (10)

Solution :

Given, (2/5x + 3/4y) (2/5x – 3/4y)

= (2/5x + 3/4y) (2/5x – 3/4y)

= (2/5x)2 – (3/4y)2

= 47/25x2 – 9/16 y

Question no – (11)

Solution :

Given, (a2 + bc) (a2 – bc)

= (a2)2 – (bc)2

= a4 – b2c

Question no – (12)

Solution :

Given, x/y + y/z) (x/y – y/z)

= (x/y)2 – (y/z)2

= x2/y2 – y2/z2

Question no – (13)

Solution :

Given, (54)2

Question no – (14)

Solution :

Given, (105)2

= (50 + 4)2

= (502 + 2.50.4 + 42

= 100 + 40 + 16

Question no – (15)

Solution :

Given, (83)2

= (100 + 5)2

= (1002) + 2.100.5 + (5)2

= 10000 + 1000 + 25

Question no – (16)

Solution :

Given, (61)2

= (60 + 1)2

= (60)2 + 2.60.1 + 12

= 3600 + 120 + 1

Question no – (17)

Solution :

Given, (69)2

= (70 – 1)2

= (70)2 – 2.70.12 + (1)2

= 4900 – 140 + 1

Question no – (18)

Solution :

Given, (49)2

= (50 – 1)2

= (50)2 – 2.80.1 + 12

= 2500 – 100 + 1

Question no – (19)

Solution :

Given, (27)2

= (30 – 3)2

= (30)2 – 2.30.3+32

= 900 – 180 + 9

Question no – (20)

Solution :

Given, (97)2

= (100 – 3)2

= (100)2 – 2.100.3 + 32

= 1000 – 600 + 9

Question no – (21)

Solution :

Given, 79 × 81

= (80 – 1) (80 + 1)

= (80)2 – 12

= 6400 – 1

= 6399

Question no – (22)

Solution :

Given, 11.1 × 10.9

= (11 + 0.1) (11 – 0.1)

= (11)2 – (0.1)2

= 121 – 0.01

= 120.99

Question no – (23)

Solution :

Given, 197 × 203

= (200 – 3) (200 + 3)

= (200)3 – 32

= 40000 – 9

= 39999

Question no – (24)

Solution :

Given, 105 × 95

= (100 + 5) (100 – 5)

= (100)2 – 52

= 1000 – 25

= 9975

Question no – (25)

Solution :

Given, (198)– (102)2

= (198 + 102) (198 – 102)

= 300 × 96

= 28800

Question no – (26)

Solution :

Given, (173)2 – (27)2

= (173 + 27) (173 – 27)

= 200 × 146

= 29200

Question no – (27)

Solution :

Here, x + 1/x = 5

or, (x + 1/x)2 = 52 = 25

or, x2 + 2. x. 1/x + (1/x)2 = 25

or, x2 + 1/x2 = 25 – 2 = 23

Question no – (28)

Solution :

Hare, x – 1/x = 11

or, (x – 1/x)2 = (11)2 = 121

or, – 2.x 1/x + (1/x)2 = 121

or, x2 + 1/x2 = 121 + 2 = 123

Question no – (29)

Solution :

= x + 1/x = 3

or, (x + 1/x)2 = 32 = 9

or, x2 + 2.x.1/x + 1/x2 = 9

or, + 1/x2 = 9 – 2 = 7

or, (x2 + 1/x)2 = 49

= x4 + 1/x = 49 – 2 = 47

= (x4 + x 1/x4) = 47

= (x2 + 1/x2)2 = 22

or, (x2)2 + 2.x2 + 1/x2 + (1/x2)2 = 4

or, x4 + 1/x4

= 4 – 2

= 2

Question no – (30)

Solution :

(x2 + 1/x2) = 49

(x – 1/x) = 2

or, (x – 1/x)2 = 22 = 4

or, x2 – 2 x.1x+ 1/x2 = 4

or,. (x2 + 1/x2)

= 4 – 2

= 2

Question no – (31)

Solution :

= (2x)2 + 2.2x.3 + 32 = (2x + b3)2

= (2.6 + 3)2 = 12 + 3

= (15)2

= 224

[ x = 6]

Question no – (32)

Solution :

= (90)2 – 2. 9a.5 + (5)2

= (9a – 5)2

= (9.3 – 5)2

= (27 – 5)2

= (22)2 = 484

Algebraic Expressions Exercise 5.4 Solution

Question no – (1)

Solution :

Given, a2b3, ab2, a2b

= a2b3 = a × a × b × b × b

= ab2 = a × b × b

= a2b = a × a × b

G.C.T = ab

Question no – (2)

Solution :

Given, 15 x3, 20x2y, – 50xy2

= 15×3 = 3 × 5 × x × x ×x

= 20x2y = 2 × 2 × 5 × x × x × x × y

= – 50xy2 = – (5 × 5 × 2 × 2 × x × y × y)

GCT = 5x

Question no – (3)

Solution :

Given, 145y4, 25x2y2, 35xy3

= 15y= 3 × 5 × y × y × y × y

= 25x2y2 = 5 × 5× x × x × y × y

= 35xy= 5 × 7 × x × y × y × y

GCT = 5y

Question no – (4)

Solution :

Given, 9ab2c, 24a2bc2, – 45a2bc

= 9ab2c = 3 × 3 × a × b × b × c

= 24a2bc2 = 3 × 2  2 × 2 × a × a × a ×b × b × c

= – 45a2bc = – 2 × 2 × 3 × 3 × a × a × a × b × c

GCT = 3abc

Question no – (5)

Solution :

Given, 24a2b2c4, 30a2b4c2, 42a5b6

= 24a2b2c= 3 × 2 × 2 × 2 × a × a × b × b × b× b

= 30a2b4c= 5 × 3 × 2 × a × a × b × b × b × b × c × c

= 42a5b= 3 × 2 × 7 × a × a × a × a × a × b × b × b × b × b × b

GCT = 3a2b2c

Question no – (6)

Solution :

Given, ax3 bx2y, cxy

= ax3 bx2y = a × x × x × x × b × x × x × y

= cxy= c × x × y × y

GCT = xy

Question no – (7)

Solution :

Given, 10x + 5y

= 5 (2x + y)

Question no – (8)

Solution :

Given,  ab2 – 4a

= a (ab – 4)

Question no – (9)

Solution :

Given, 3x2 y – 9xy2

= 3xy (x – 3y)

Question no – (10)

Solution :

Given, 5ab + 15b2

= 5b (a + 3b)

Question no – (11)

Solution :

Given, 13 x3y5 – 65 x4y4

= 13x3y4 (y – 5x)

Question no – (12)

Solution :

Given, 18×3 + 24x2y

= 6x2 (3x + 4y)

Question no – (13)

Solution :

Given, 4×2 + 20xy + 25y2

= (2x)2 + 2. 2x. 5y + (5y)2

= (2x + 5y)

Question no – (14)

Solution :

Given, 1 + 6yz + 9y2x2

= 12 + 2.13yz + (3yz)2

= (1 + 3yz)

Question no – (15)

Solution :

Given, 7a3 + 28a2 + 28a

= 7a (a2 + 4a + 4)

= 7a [a2 + 2.a.2 + 22]

= 7a (a + 2)2

Question no – (16)

Solution :

Given, 2a2b2 + 8ab + 8

= 2 (a2 b2 + 4ab + 4)

= 2 [(ab)2 + 2.ab.2 + 22]

= 2 (ab + 2)2

Question no – (17)

Solution :

Given, 9p2 – 30pq + 25q2

= (3p)2 – 2.3p.5q2

= (3p – 5q)2

Question no – (18)

Solution :

Given, 4×2 – 4xy + y2

= (2x)2– 2.2x.y+ y2

= (2x – y)2

Question no – (19)

Solution :

Given, x3 – 6×2 y + 9xy2

= x (x2 – 6xy + 9y2)

= x (x2 – 2.x.3y + (3y)2]

= x (x + 3y)2

Question no – (20)

Solution :

Given, a2 – 8ab + 16b2

= a2 – 2.a.4b + (4b)2

= (a – 4b)2

Question no – (21)

Solution :

Given, 1 – 49x2y2

= (1)2 – (7xy)2

Question no – (22)

Solution :

Given, (a + b)2 – (a – b)2

= (a + b + a – b) (a + b – a + b)

= 2a × 2b

= 4ab

Question no – (23)

Solution :

Given, 4x2 – 9y2

= (2x)2 – (3y)2

= (2x + 3y) (2x – 3y)

Question no – (24)

Solution :

Given, 36a2b2 – 49c2

= (6ab)2 – (7c)2

= (6ab + 7c) (6ab – 7c)

Question no – (25)

Solution :

Given, x4 – y4

= (x2) – (y2)2

= (x2 + y2) (x2 – y2)

= (x2 + y2) (x + y) (x – y)

Question no – (26)

Solution :

Given, (a4 – 6a2 + 9) – 144

= (a2 + 3)2 – (11)2

= (a2 + 3 + 11) (a2 + 3 – 11)

= (a2 + 14) (a2 – 8)

Question no – (27)

Solution :

Given, x2 – (y + z)2

= (x + y + z) (x – y + z)

Question no – (28)

Solution :

Given, 3×3 – 75×5

= 3x3(1 – 25x2)

= 3x2 [12 – (5x)2]

= 3x2(1 + 5x) (1 – 5x)

Next Chapter Solution :

Updated: June 10, 2023 — 5:15 am