Brilliant’s Composite Mathematics Class 7 Solutions Chapter 5

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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)

= 10x² + 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) (x² + 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)

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

= 4p² – 3q² – 6p² + pq + 12q²

= – 2p² + 15q² …(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

= 4x² + 12xy + 9y² 

Question no – (2)

Solution : 

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

= (3a + 4b)²

= (3a)² + 2.3a. 4b + (4b)²

= 9a² + 24ab + 6b² 

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 + 25q² 

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 + 2x²y² + 25/4y⁴ 

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 a² – 3/5 ab + 4/25 b² 

Question no – (7)

Solution : 

Given, (2x – 7y) (2x – 7y)

= (2x – 7y)²

= (2x)² – 2.2x.7y + (7y)²

= 4x² – 28xy + 49y² 

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)² – (3a)²

= 4p² – 9q² 

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 y² 

Question no – (11)

Solution : 

Given, (a² + bc) (a² – bc)

= (a²)² – (bc)²

= a⁴ – b²c² 

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)² – (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

= 15y⁴ = 3 × 5 × y × y × y × y

= 25x²y² = 5 × 5× x × x × y × y

= 35xy³ = 5 × 7 × x × y × y × y

∴ GCT = 5y² 

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

= 24a²b²c⁴ = 3 × 2 × 2 × 2 × a × a × b × b × b× b

= 30a²b⁴c² = 5 × 3 × 2 × a × a × b × b × b × b × c × c

= 4²a⁵b⁶ = 3 × 2 × 7 × a × a × a × a × a × b × b × b × b × b × b

∴ GCT = 3a²b²c² 

Question no – (6)

Solution : 

Given, ax³ bx²y, cxy² 

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

= cxy² = 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)² 

Question no – (14)

Solution : 

Given, 1 + 6yz + 9y²x²

= 12 + 2.13yz + (3yz)²

= (1 + 3yz)² 

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 : 

👉 Chapter 6 👈