Joy of Mathematics Class 6 Solutions Chapter 10

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Joy of Mathematics Class 6 Solutions Chapter 10 Operations on Algebraic Expressions

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 10 Operations on Algebraic Expressions. Here students can easily find step by step solutions of all the problems for Operations on Algebraic Expressions. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 10 solutions. Here students will find exercise wise solutions for chapter 10 Exercise 10.1, 10.2, 10.3, 10.4, 10.5 and 10.6

Operations on Algebraic Expressions Exercise 10.1 Solution :

Question no – (1) 

Solution :

(a) (2x + 5x)

= 7x

(b) (3x + 7x)

= 10x

(c) (5x + 3x)

= 8x

(d) 5a² + (-9a²)

= 5a² – 9a²

= – 4a²

(e) 3xy + (-xy)

= 3xy – xy

= 2 xy

(f) 3xyz + 2xyz – xyz

= 5xyz – xyz

= 4xyz

(g) 6a² + (- 8a²) + (-2) + 10a²

= 6a² – 8a² – 2 + 10a²

= 8a² – 2

(h) 5ab + (- 3ab) + ab

= 5ab – 3ab + ab

= 3ab

(i) a + b + 3a + 2b

= 4a + 3b

(j) 5x²y² + 7x²y² + 3x²y²

= 15x²y²

(k) 5a + 2a + (-3a) + 4

= 7a – 3a + 4

= 4a + 4

= 4(a + 1)

(l) a⁴ + (-3a⁴) + (-7a⁴) + (-4a⁴)

= a⁴ – 3a⁴ – 7a⁴ – 4a⁴

= – 13a⁴

Question no – (2) 

Solution : 

(a) 2a + 3b – 9

4a – 6b

–  3a + 2b

6a – 2b
———————————
15a – 3b – 9

(b) 5a – 6b

+ 7a + 8b

-5a + 2b
———————————
7a + 4b

(c) 18a – 10b

-2a + 12b

+  -10a + 6b
———————————
6a + 8b

(d) -15a – 6b

-3a + 5b

+ 16a – 10b
———————————
– 2a – 11b

(e) a + b – 3c

2a – b + 7c

+ a – 4b
———————————
4a – 4b + 4c

(f) a – b – c

2a – 5b + 7c

+ -a –b +3c
———————————
2a – 7b + 9c

Question no – (3) 

Solution :

(a) (x³ – x² + 7) + (-9x + 10x² – 6) + (2x – 3x² – 5)

= x³ – x² + 7 – 9x + 10x² – 6 + 2x – 3x² – 5

= x³ + 6x² – 4

(b) (2x² – 4x – 3) + (5x – 6x² + 2) + (6x – 3 + 5x²)

= 2x² – 4x – 3 + 5x – 6x² + 2 + 6x – 3 + 5x²

= x² + 7x – 4

(c) (9x² – 10x – 10) + (- 15x + 10x² – 5) + (5x² – 6x + 15)

= 9x² – 10x – 10 – 15x + 10x² – 5 + 5x² – 6x + 15

= 24x² – 31x

(d) (10x² – 15x – 12) + (-15x² + 14x + 16) + (16x² – 5x + 25)

= 10x² – 15x – 12 – 15x² + 14x + 16 + 16x² – 5x + 25

= 11x² – 6x + 29

Question no – (4) 

Solution :

(a) x – 3y + 2z

3x + 7y – 4z

2x + 2y – 3z
———————————
6x + 6y – 5z

(b) 2x – 3y + 4z

3x + y – z

– x – y – 2z
———————————
4x – 3y + z

(c) xy + yz + zx

2xy + 3yz – 4zx

– xy – 6yz + zx
———————————
2xy – 2yz – 2zx

(d) 3x² + 3y² + 4xy

2x² + 5y² – xy

-4x² – 7y² – xy
———————————
x² + y² + 2xy

Question no – (5)

Solution :

Sum of = (3a2 + 2a) + (7 – 3a)

= 3a2 + 2a + 7 – 3a

= 3a2 – a + 7

Now, (2a² – 3a² + 1) + (3a² – a + 7)

= 2a² – 3a² + 1 + 3a² – a + 7

= 2a² – a + 8

Question no – (6)

Solution :

A + B + C

= (a² – b² + 2ab) + (a² + 4b² – 6ab) + (a² + 4ab)

= a² – b² + 2ab + a² + 4b² – 6ab + a² + 4ab

= 3a² + 3b²

Question no – (7)

Solution :

A + B + C

= 3x² + 5x – 8y² + x² – 4x – 2 + (-5x² – 4x² + 2)

= 3x² + 5x – 8y + x² – 4x – 2 – 5x² – 4x² + 2

= – 5x² – 8y² + x

Operations on Algebraic Expressions Exercise 10.2 Solution :

Question no – (1) 

Solution :

(a) (8x – 5x)

= 3x

(b) (-8x – 4x)

= – 12x

(c) {3y – (-5y)}

= 3y + 5y

= 8y

(d) [-12x – (-5x)]

= – 12x + 5x

= – 7x

(e) [- 12pq – (-5pq)]

= – 12pq + 5pq

= -7pq

(f) (7ab² – 3ab²)

= 4ab²

Question no – (2) 

Solution :

(a) (7a – 7) – (3a + 5)

= 7a – 7 – 3a – 5

= 4a – 12

(b) (3a² – 7ab) – (a² – 3ab)

= 3a² – 7ab – a² + 3ab

= 2a² – 4ab

(c) (5a – 8b) – (2a – 3b)

= 5a – 8b – 2a + 3b

= 3a – 5b

(d) (7a – 8b) – (5a – 6b)

= 7a – 8b – 5a + 6b

= 2a – 2b

(e) (6a – 10a²) – (9a² – 3a)

= 6a – 10a² – 9a² + 3a

= – 19a² + 9a

(f) (-10a – 6a²) – (10a² – 5a)

= – 10a – 6a² – 10a² + 5a

= – 16a² – 5a

Question no – (3)

Solution :

Sum of

= (2a + 4b + 7c) + (2a – 5b + 3c)

= 2a + 4b + 7c + 2a – 5b + 3c

= 4a – b + 10c

Now, (4a – b + 10c) – (a + 2b – 3c)

= 4a – b + 10c – a – 2b + 3c

= 3a – 3b + 13c

Question no – (4)

Solution :

Should be increase

= (x² – y² + 3xy) – (4x² + y² + 4xy)

= x² – y² + 3xy – 4x² – y² – 4xy

= – 3x² – 2y² – xy

Question no – (5)

Solution :

Should be subtracted

= (4x² – 2xy + y²) – (-3x² + 4xy – y²)

= 4x² – 2xy + y² + 3x² – 4xy + y²

= 7x² – 6xy + 2y²

Question no – (6)

Solution :

Here, (7a – 3b + 4ab) – (2a + 3b – 4ab)

= 7a – 3b + 4ab – 2a – 3b + 4ab

= 5a – 6b + 8ab

Question no – (7)

Solution :

(4x – y + 3z) – (2x + 7y – 4z)

= 4x – y + 3z – 2x – 7y + 4z

= 2x – 8y + 7z

Question no – (8)

Solution :

Sum of

= (4x² – 6x + 3) + (-4x³ – 7x + 5)

= 4x² – 6x + 3 – 4x² – 7x + 5

= – 13x + 8

Question no – (9)

Solution :

Number must be added,

= (2x³ – x² + 4x – 1) – (3x³ – 2x² + 5x + 1)

= 2x³ – x² + 4x – 1 – 3x³ + 2x² – 5x – 1

= – x³ + x² – x

Question no – (10)

Solution :

Number must be subtracted,

= (3x² – 2xy + 6y²) – (-4x² – 2xy – y²)

= 3x² – 2xy + 6y² + 4x² + 2xy + y²

= 7×2 + 7y²

= 7x² + 7y²

Operations on Algebraic Expressions Exercise 10.3 Solution :

Question no – (1) 

Solution :

(a) 3x × 4x

= 12x²

(b) 3x × 4y

= 12xy

(c) 2×2 × 3y2

= 6x²y²

(d) xy × x²y

= x³y²

(e) 0 × 2xy

= 0

(f) (-6x²) × (-4xy²)

= 24x³y²

(g) xy (x + y)

= x²y + xy²

(h) (3a² – b²) × 4ab

= 12a³b – 4ab³

(i) 3xy² × (xy – 5x)

= 3x²y³ – 15x²y²

(j) (1 + x) 3x

= 3x + 3x²

(k) (3x + 2y) 2xy

= 6x²y + 4xy²

(l) (3x² – 2xy²) × (-2xy)

= 6x³y² + 4x²y³

Question no – (2) 

Solution :

(a) (x + y + z) 2xyz

= 2x²yz + 2xy²z + 2xyz²

(b) (xy + yz + zx) x²yz²

= x³y²z² + x²y²z³ + x³yz³

(c) (x² + y² + 3z²) 6x

= 6x³ + 6xy + 18xz²

(d) (a + b + c) a²b²c²

= a³b²c² + a²b³c² + a²b²c³

(e) (3x²y + 2y²z – xy²) xyz

= 3x³y²z + 2xy³z² – x²y³z

(f) (m² + n² + p²) 2mn

= 2m³n + 2mn³ + 2mnp²

Question no – (3) 

Solution :

(a) (x + y) (2x + 3y)

= 2x² + 3xy + 2xy + 3y²

= 2x² + 5xy + 3y²

(b) (x – y) (2x – 3y)

= 2x² – 3xy – 2xy + 3y²

= 2x² – 5xy + 3y²

(c) (x + y) (x – y)

= x² – xy + xy – y²

= x² – y²

(d) (2x + 3y) (3y – 4x)

= 6xy – 8x² + 9y² – 12xy

= 6xy – 12xy – 8x² + 9y²

= – 6xy – 8x² + 9y²

(e) (2x² – 3x³) (x³ + x²)

= 2x⁵ + 2x⁴ – 3x⁶ – 3x⁵

(f) (2x² – y²) (3x² + 4y²)

= 6x⁴ + 8x²y² – 3x²y² – 4y⁴

Question no – (4) 

Solution :

(a) (x – 3) (2x + 3)

= 2x² + 3x – 6x – 9

= 2x² – 3x – 9

(b) (x – y) (x² + y²)

= x³ + xy² – x²y – y³

= x³ – y³ + y(xy – x)

(c) (2x – 3) (2x + 3)

= 4x² + 6x – 6x – 9

= 4x² – 9

(d) (2x + 3) (2x + 3)

= 4x² + 6x + 6x + 9

= 4x² + 12x + 9

(e) (2x – 3) (2x – 3)

= 4x² – 6x – 6x + 9

= 4x² – 12x + 9

(f) (3x – 1) (3x + 4)

= 9x² + 12x – 3x – 4

= 9x² + 9x – 4

Operations on Algebraic Expressions Exercise 10.4 Solution :

Question no – (1) 

Solution :

(a) 12a³/4a²

= 3a

(b) 8a⁴/-4a³

= – 2a

(c) 9a³/3a

= 3a²

(d) 15xy/5x

= 3y

(e) -45x³y²/9x²y

= – 5xy

(f) 6a²b/6ab²

= a/b

(g) 2x² + 8/2

= x² + 4

(h) 25x² + 15x/5x

= 5x + 3

(i) 12a² + 8a/4a

= 3a + 2

Question no – (2) 

Solution :

(a) 2x⁵/x³

= 2x²

(b) 0.6x⁴/1.2x

= 0.5x³

(c) 2.48xy/-8xy

= – 0.31

(d) -75x³y/25x²

= – 3xy

(e) – 45x³y²/9x²y

= – 5xy

(f) 40x³y³z⁴/8x³z³

= 5y³z

Question no – (3) 

Solution :

(a) 18a³b³ + 24a⁴b⁵ – 30a⁵b⁶/- 6a³b³

= – 3 – 4ab² + 5a²b³

(b) 14a³b⁷ + 35a⁴b⁶ – 42a²b⁴/- 7a²b⁴

= – 2ab³ – 5a²b² + 6

(c) a²bc + ab²c – 3abc²/abc

= a + b – 3c

(d) x³y³ + x⁴y² + 3x²y + 3xy²/xy

= x²y² + x³y + 3x + 3y

Operations on Algebraic Expressions Exercise 10.5 Solution :

Question no – (1) 

Solution :

(a) a^b

= 3²

= 9

(b) b^a

= 2³

= 8

(c) ab

= 3 × 2

= 6

(d) a/b

= 3/2

Question no – (2) 

Solution :

(a) 2x – 3y

= 2 × 3 – 3 × (-2)

= 6 × 6

= 12

(b) a + b – 2c

= 3 + 2 – 2y (- 1)

= 3 + 2 + 2

= 7

(c) 2p + 2q – 4r

= 2 × 1 + 2 × 2 – 4 × (-6)

= 2 + 4 + 24

= 30

(d) 2ab + 3bc – 4ac

= 2 × 1 × (-2) + 3 × (-2) × 3 – 4 × 1 × (3)

= – 4 – 18 – 12

= – 34

(e) p – q – r

= 1 – (-1) – (-3)

= 1 + 1 + 3

= 5

(f) 3xy – 4yz – xz

= 3 × 1 × (-2) – 4 × (-2) × (-3) – 1 × (-3)

= – 6 – 24 + 3

= – 27

Question no – (3) 

Solution :

(a) 2x² – 7x + 5

= 2 × 3² – 7 × 3 + 5   [x = 3]

= 2 × 9 – 21 + 5

= 18 – 21 + 5

= 2

(b) 3x³ – 4x² + 5x

= 3 × (-2)³ – 4 × (-2)² + 5 × (-2)

= – 24 – 16 – 10

= – 50

(c) x⁴ + x³ – 5x + 7

= (-3)⁴ + (-3)³ – 5 × (-3) + 7

= 81 – 27 + 15 + 7

= 76

(d) 3x² – 4x + 7

= 3 × (1)² – 4 × 1 + 7

= 3 – 4 + 7

= 6

Question no – (4)

Solution :

(a) x² + 2xy + y² + z²

= (x + y)² + z²

= (2 + 1)² + (- 3)²

= 3² + 9

= 9 + 9

= 18

(b) (x + y – z)³

= (2 + 1 + 3)³

= (6)³

= 216

(c) x² + 4y² + z² – 4xy – 4yz + 2xz

= 2² + 4 × 1² + (-3)² – 4 × 2 × 1 – 4 × 1 × (-3) + 2 × 1 × (-3)

= 4 + 4 + 9 – 8 + 12 – 6

= 15

(d) x² + y² + z² + 2xy + 2yz + 2zx
= (x + y + z)²
= (2 + 1 – 3)
= 0²
= 0

(e) x³ + y³ + z³ – 3xyz

= 2³ + 1³ + (-3)³ – 3 × 2 × 1 × (-3)

= 8 + 1 – 27 + 18

= 0

(f) x² + 4y – 3z/xyz

= 2² + 4 × 1 – 3 × (-3)/2 × 1 × (-3)

= 4 + 4 + 9/-6

= 17/-6

Question no – (5)

Solution :

(a) 2p² + q² + r² – 3pqr

= 2 × (1)² + (2)² + (-3)² – 3 × 1 × 2 × (-3)

= 2 + 4 + 9 + 18

= 33

(b) p³ + q³ – r³

= (1)³ + (2)³ + (-3)³

= 1 + 8 – 27

= – 18

(c) 3.5p⁵ + 0.4q – 12.6r³/pqr

= 3.5 × 15 + 0.4 × 2 – 12.6 × (-3)³/1 × 2 × (-3)

= 3.5 + 0.8 – 12.6 × (-27)/-6

= 3.5 + 0.8 – 340.2/-6

= 55.98

Question no – (6)

Solution :

m⁴n + n⁴m + mnp – p³

= 1⁴ × 2 + 2⁴ × 1 + 1 × 2 × (-3) – (-3)³

= 1 + 16 – 6 + 27

= 39

Operations on Algebraic Expressions Exercise 10.6 Solution :

Question no – (1)

Solution : 

(4a + 11b) + {2a – 3b – (4a – 2b)}

= (4a + 11b) + {2a – 3b – 4a + 2b}

= 4a + 11b + (- 2a – b)

= 4a + 11b – 2a – b

= 2a + 10b

Question no – (2)

Solution :

[6a – 17b² – {7a – 3b – (5a + 5b)}]

= 6a – 17b² – {17a – 3b – 5a – 5b}

= 6a – 17b² – {2a – 8b}

= 6a – 17b² – 2a + 8b

= 4a + 8b – 17b2

Question no – (3)

Solution :

(2a – 17b) + [2a – 3b – {2a – 3b – (4a – 2b)}]

= (2a – 17b) + [2a – 3b – {2a – 3b – 4a + 2b}]

= (2a – 17b) + [2a – 3b – {-2a – b}]

= (2a – 17b) + [2a – 3b + 2a + b]

= (2a – 17b) + [4a – 2b]

= 2a – 17b + 4a – 2b

= 6a – 19b

Question no – (4)

Solution :

4a – [3a – b – {2a – 3b – (2a + 5 – a)}]

= 4a – [3a – b – {2a – 3b – (a + 5)}]

= 4a – [3a – b – {2a – 3b – a – 5}]

= 4a – [3a – b – {a – 3b – 5}]

= 4a – [3a – b – a + 3b + 5]

= 4a – [2a + 2b + 5]

= 4a – 2a – 2b – 5

= 2a – 2b – 5

Question no – (7)

Solution :

3a + 5b – [2a – 3b – {5a – 6b – (2a – 3b)}]

= 3a + 5b – [2a – 3b 0 {5a – 6b – 2a + 3b}]

= 3a + 5b – [2a – 3b – 3a + 3b]

= 3a + 5b + a

= 4a + 5b

Question no – (8)

Solution :

2a – [4b – {4a – (3b – 2a + 2b)}]

= 2a – [4b – {4a – (3b – 2a – 2b)}]

= 2a – [4b – {4a – 3b + 2a + 2b}]

= 2a – [4b – {6a – b}]

= 2a – [4b – 6a + b]

= 2a – [5b – 6a]

= 2a – 5b + 6a

= 8a – 5b

Question no – (9)

Solution :

2a – 9b – [6a – 5b + {7a – 12b – (2a – 13b – 4c)}]

= 2a – 9b – [6a – 5b + {7a – 12b – (2a – 3b + 4c)}]

= 2a – 9b – [6a – 5b + {7a – 12b – 2a + 3b – 4c}]

= 2a – 9b – [6a – 5b + 7a – 12b – 2a – 3b – 4c]

= 2a – 9b – 11a + 20b + 4c

= – 9a + 11b + 4c

Question no – (10)

Solution : 

– 3a – {2a + 5b – (a – b)} – 6a – (3a – 4a + b)

= – 3a – {2a + 5b – (a – b)} – 6a – (3a – 4a – b)

= – 3a – {2a + 5b – a + b} – 6a – 3a + 4 + b

= – 3a – {a + 6b} – 5a + 5b

= – 3a – a – 6b – 5a + 5b

= – 9a – b

Next Chapter Solution : 

👉 Chapter 11 👈