RS Aggarwal Solutions for Class 6 Chapter 8 Exercise 8C are available in PDF format for free download. Subtraction of Algebraic Expressions is the topic that is covered under this exercise. Students can refer to the solutions to get a better understanding of the concept. These solutions provide accurate answers which are easily understood by the students. Practicing problems using RS Aggarwal solutions increase the capacity of answering at a good speed. Download PDF from their respective links.

## Download PDF of RS Aggarwal Solutions for Class 6 Chapter 8 Algebraic Expressions Exercise 8C

### Access answers to Maths RS Aggarwal Solutions for Class 6 Chapter 8 Algebraic Expressions Exercise 8C

**1. Add: **

**(i) 3x, 7x**

**(ii) 7y, -9y**

**(iii) 2xy, 5xy, -xy**

**(iv) 3x, 2y**

**(v) 2x ^{2}, -3x^{2}, 7x^{2}**

**(vi) 7xyz, -5xyz, 9xyz, -8xyz**

**(vii) 6a ^{3}, -4a^{3}, 10a^{3}, -8a^{3}**

**(viii) x ^{2} â€“ a^{2}, – 5x^{2} + 2a^{2}, -4x^{2} + 4a^{2}**

**Solutions**

**(i) **The required sum = 3x + 7x

= (3 + 7) x

= 10x

(ii) The required sum = 7y + (-9y)

= 7y â€“ 9y

= (7 -9) y

= -2y

(iii) The required sum = 2xy + 5xy + (-xy)

= 2xy + 5xy â€“ xy

= (2x + 5x â€“x) y

= 6xy

(iv) The required sum = 3x + 2y

= 3x + 2y

(v) The required sum = 2x^{2} + (-3x^{2}) + 7x^{2}

^{ } = 2x^{2} – 3x^{2} + 7x^{2}

= (2 – 3 + 7) x^{2}

= 6x^{2}

(vi) The required sum = 7xyz + (-5xyz) + 9xyz + (-8xyz)

= 7xyz â€“ 5xyz + 9xyz â€“ 8xyz

= (7 â€“ 5 + 9 â€“ 8) xyz

= (16 â€“ 13) xyz

= 3xyz

(vii) The required sum = 6a^{3}** ^{ }**+ (-4a

^{3}) + 10a

^{3 }+ (-8a

^{3})

= 6a^{3 }â€“ 4a^{3 }+ 10a^{3} â€“ 8a^{3}

= (6 â€“ 4 + 10 â€“ 8) a^{3}

^{ }= (16 â€“ 12) a^{3}

= 4a^{3}

(viii) The required sum = (x^{2 }â€“ a^{2})^{ }+ (-5x^{2} + 2a^{2}) + (-4x^{2 }+ 4a^{2})

= x^{2}– a^{2} â€“ 5x^{2 }+ 2a^{2} â€“ 4x^{2 }+ 4a^{2}

= (1 â€“ 5 â€“ 4) x^{2 }â€“ (1 â€“ 2 â€“ 4) a^{2}

= (1 â€“ 9) x^{2 }â€“ (1 â€“ 6) a^{2}

^{ }= -8x^{2 }+ 5a^{2}

**2. Add the following:**

**(i) x â€“ 3y â€“ 2z (ii) m ^{2} â€“ 4m + 5 (iii) 2x^{2} â€“ 3xy + y^{2} **

** 5x + 7y â€“ z -2m ^{2} + 6m â€“ 6 – 7x^{2} â€“ 5xy â€“ 2y^{2}**

** -7x â€“ 2y + 4z -m ^{2} â€“ 2m â€“ 7 4x^{2} + xy â€“ 6y^{2}**

** __________ __________ ____________**

** __________ __________ ____________**

**(iv) 4xy â€“ 5yz â€“ 7z**

** – 5xy +2yz + zx**

** – 2xy -3yz +3zx**

** ____________**

** ______________**

**Solutions**

**(i) **x â€“ 3y â€“ 2z

5x + 7y â€“ z

-7x â€“ 2y + 4z

____________________

-x + 2y + z

____________________

(ii) m ^{2}â€“ 4m + 5

-2m^{2 }+ 6m â€“ 6

– m^{2 }– 2m â€“ 7

_______________

-2m^{2} +0m â€“ 8

= -2m^{2} – 8

________________

(iii) 2x^{2 }â€“ 3xy + y^{2}

^{ } -7x^{2 }â€“ 5xy â€“ 2y^{2}

^{ } 4x^{2} + xy â€“ 6y^{2}

^{ ___________________________}

^{ } -x^{2 }â€“ 7xy â€“ 7y^{2}

^{ _____________________________}

(iv) 4xy â€“ 5yz â€“ 7zx

-5xy + 2yz + zx

-2xy â€“ 3yz + 3zx

_________________

-3xy -6yz -3zx

________________

**3. Add:**

**(i) 3a â€“ 2b + 5c, 2a +5b â€“ 7c, – a â€“ b + C**

**(ii) 8a â€“ 6ab + 5b, – 6a â€“ ab â€“ 8b, – 4a + 2ab + 3b**

**(iii) 2x ^{3} â€“ 3x^{2} + 7x â€“ 8, – 5x^{3} + 2x^{2} â€“ 4x + 1, 3 â€“ 6x + 5x^{2} â€“ x^{3}**

**(iv) 2x ^{2} â€“ 8xy + 7y^{2} â€“ 8xy^{2}, 2xy^{2} + 6xy â€“ y^{2} + 3x^{2}, 4y^{2} â€“ xy â€“ x^{2} + xy^{2}**

**(v) x ^{3} + y^{3} – z^{3} + 3xyz, -x^{3} + y^{3} + z^{3} â€“ 6xyz, x^{3} â€“ y^{3} â€“ z^{3} â€“ 8xyz**

**(vi) 2 + x â€“ x ^{2} + 6x^{3}, – 6 â€“ 2x + 4x^{2} â€“ 3x^{3}, 2 + x^{2}, 3-x^{3} + 4x â€“ 2x^{2}**

**Solution**

**(i) **The sum of the given expressions

= (3a + 2a â€“a) + (-2b +5b â€“b) + (5c â€“ 7c +c)

= 4a + 2b â€“ c

(ii) The sum of the given expressions

= (8a -6a -4a) + (5b â€“ 8b + 3b) + (-6ab â€“ab + 2ab)

= -2a â€“ 5ab

(iii) The sum of the given expressions

= (2x^{3} â€“ 5x^{3} â€“ x^{3}) + (-3x^{2} + 2x^{2} + 5x^{2}) + (7x – 4x â€“ 6x) + (-8 + 1 +3)

= – 4x^{3 }+ 4x^{2 }â€“ 3x – 4

(iv) The sum of the given expressions

** = **(2x^{2 }+ 3x^{2 }â€“ x^{2}) + (-8xy + 6xy â€“ xy) + (7y^{2 }â€“ y^{2 }+ 4y^{2}) + (-8xy^{2} + 2xy^{2 }+ xy^{2})

= 4x^{2} â€“ 3xy + 10 y^{2 }â€“ 5xy^{2}

(v) The sum of the given expressions

= (x^{3 }– x^{3 }+ x^{3}) + (y^{3} + y^{3} â€“ y^{3}) + (-z^{3} + z^{3 }â€“ z^{3}) + (3xyz â€“ 6xyz â€“ 8xyz)

= x^{3} + y^{3} â€“ z^{3} â€“ 11xyz

(vi) The sum of the given expressions

= (2 â€“ 6 + 2 + 3) + (x â€“ 2x + 4x) + (- x^{2} + 4x^{2} + x^{2} â€“ 2x^{2}) + (6x^{3 }â€“ 3x^{3} â€“ x^{3})

= 1 + 3x + 2x^{2} + 2x^{3}

**4. Subtract:**

**(i) 5x from 2x**

**(ii) – xy from 6xy**

**(iii) 3a from 5b**

**(iv) – 7x from 9y**

**(v) 10x ^{2} from – 7x^{2}**

**(vi) a ^{2} â€“ b^{2} from b^{2} â€“ a^{2}**

**Solutions**

**(i) **Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = 5x

Changing the sign of each term of expression = -5x

2x â€“ 5x = (2 â€“ 5) x

= – 3x

(ii) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = -xy

Changing the sign of each term of expression = xy

6xy + xy = (6 + 1) xy

= 7xy

(iii) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = 3a

Changing the sign of each term of expression = – 3a

= (5b â€“ 3a)

(iv) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = – 7x

Changing the sign of each term of expression = 7x

= (9y + 7x)

(v) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = 10x^{2}

Changing the sign of each term of expression = – 10x^{2}

^{ }= (- 7x^{2} â€“ 10x^{2})

= – 17x^{2}

(vi) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

We get

Term which is subtracted = a^{2} â€“ b^{2}

Changing the sign of each term of expression = – (a^{2} â€“ b^{2})

= (b^{2 }â€“ a^{2}) â€“ (a^{2 }â€“ b^{2})

= (b^{2} â€“ a^{2} â€“ a^{2} + b^{2})

= 2b^{2 }â€“ 2a^{2}

**5. Subtract: **

**(i) 5a + 7b â€“ 2c from 3a â€“ 7b + 4c**

**(ii) a â€“ 2b -3c from -2a + 5b â€“ 4c**

**(iii) 5x ^{2} â€“ 3xy + y^{2} from 7x^{2} â€“ 2xy â€“ 4y^{2}**

**(iv) 6x ^{3} â€“ 7x^{2} + 5x â€“ 3 from 4 – 5x + 6x^{2} â€“ 8x^{3}**

**(v) x ^{3} + 2x^{2}y + 6xy^{2} â€“ y^{3} from y^{3} â€“ 3xy^{2} â€“ 4x^{2}y**

**(vi) – 11x ^{2}y^{2} + 7xy â€“ 6 from 9x^{2}y^{2} â€“ 6xy + 9**

**(vii) -2a + b + 6d from 5a -2b -3c**

**Solutions**

**(i) **Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = 5a + 7b – 2c

Changing the sign of each term of expression = – 5a â€“ 7b + 2c

Now add

= (3a â€“ 7b + 4c) + (- 5a – 7b + 2c)

= 3a â€“ 5a â€“ 7b – 7b + 4c + 2c

= -2a â€“ 14b + 6c

(ii) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = a â€“ 2b â€“ 3c

Changing the sign of each term of expression = -a + 2b + 3c

Now add

= (- 2a + 5b – 4c) + (-a + 2b + 3c)

= -2a + 5b â€“ 4c â€“ a + 2b + 3c

= -3a + 7b â€“ c

(iii) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = 5x^{2} â€“ 3xy + y^{2}

Changing the sign of each term of expression = – 5x^{2 }+ 3xy â€“ y^{2}

Now add

= (7x^{2 }– 2xy â€“ 4y^{2}) + (- 5x^{2} + 3xy â€“ y^{2})

= 7x^{2} â€“ 2xy â€“ 4y^{2} â€“ 5x^{2 }+ 3xy â€“ y^{2}

= 2x^{2} + xy â€“ 5y^{2}

(iv) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = 6x^{3} – 7x^{2} + 5x – 3

Changing the sign of each term of expression = -6x^{3} + 7x^{2} â€“ 5x + 3

Now add

= (4 â€“ 5x + 6x^{2} â€“ 8x^{3}) + (- 6x^{3} + 7x^{2} â€“ 5x + 3)

= 4 â€“ 5x + 6x^{2} â€“ 8x^{3 }â€“ 6x^{3} + 7x^{2} â€“ 5x + 3

= 4 + 3 â€“ 5x â€“ 5x + 6x^{2}_{ }+ 7x^{2} â€“ 8x^{3} â€“ 6x^{3}

= 7 â€“ 10x + 13x^{2} â€“ 14x^{3}

(v) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = x^{3} + 2x^{2}y + 6xy^{2} â€“ y^{3}

Changing the sign of each term of expression = -x^{3} â€“ 2x^{2}y â€“ 6xy^{2} + y^{3}

Now add

= (y^{3} â€“ 3xy^{2} â€“ 4x^{2}y) + (- x^{3} â€“ 2x^{2}y â€“ 6xy^{2} + y^{3})

= y^{3} â€“ 3xy^{2} â€“ 4x^{2}y â€“ x^{3} â€“ 2x^{2}y â€“ 6xy^{2} + y^{3}

= y^{3} + y^{3} â€“ 3xy^{2} â€“ 6xy^{2} â€“ 4x^{2}y â€“ 2x^{2}y â€“ x^{3}

^{ }= 2y^{3} â€“ 9xy^{2} â€“ 6x^{2}y â€“ x^{3}

(vi) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = -11x^{2}y^{2} + 7xy – 6

Changing the sign of each term of expression = 11x^{2}y^{2 }â€“ 7xy + 6

Now add

= (9x^{2}y^{2} â€“ 6xy + 9) + (11x^{2}y^{2} â€“ 7xy + 6)

= 9x^{2}y^{2} â€“ 6xy + 9 + 11x^{2}y^{2} â€“ 7xy + 6

= 9x^{2}y^{2} + 11x^{2}y^{2} â€“ 6xy â€“ 7xy + 9 + 6

= 20x^{2}y^{2} â€“ 13xy + 15

(vii) Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = -2a + b + 6d

Changing the sign of each term of expression = 2a â€“ b â€“ 6d

Now add

= (5a â€“ 2b â€“ 3c) + (2a â€“ b â€“ 6d)

= 5a â€“ 2b â€“ 3c + 2a â€“ b â€“ 6d

= 5a + 2a â€“ 2b â€“ b â€“ 3c â€“ 6d

= 7a â€“ 3b â€“ 3c â€“ 6d

** **

**6. Simplify:**

**(i) 2p ^{3} â€“ 3p^{2} + 4p â€“ 5 â€“ 6p^{3} + 2p^{2} â€“ 8p -2 + 6p +8**

**(ii) 2x ^{2} â€“ xy + 6x â€“ 4y + 5xy â€“ 4x + 6x^{2} + 3y**

**(iii) x ^{4} â€“ 6x^{3} + 2x â€“ 7 + 7x^{3} â€“ x + 5x^{2} + 2 â€“ x^{4}**

**Solution**

**(i) **Given

2p^{3} â€“ 3p^{2} + 4p â€“ 5 â€“ 6p^{3} + 2p^{2} â€“ 8p â€“ 2 + 6p + 8

** **Rearranging and collecting the like terms, we get:

= 2p^{3} â€“ 6p^{3} â€“ 3p^{2} + 2p^{2} + 4p â€“ 8p + 6p â€“ 5 + 2 + 8

= (2 â€“ 6) p3 â€“ (3 â€“ 2) p2 + (4 â€“ 8 + 6) p â€“ (5 – 2 â€“ 8)

= (- 4) p^{3} â€“ (1) p^{2} + (10 â€“ 8) p â€“ (7 â€“ 8)

= (-4) p^{3} â€“ p^{2} + (2) p â€“ (-1)

= – 4p^{3 }â€“ p^{2} + 2p + 1

(ii) Given

2x^{2} â€“ xy + 6x â€“ 4y + 5xy â€“ 4x + 6x^{2} + 3y

Rearranging and collecting the like terms, we get:

= 2x^{2} + 6x^{2} â€“ xy + 5xy + 6x â€“ 4x â€“ 4y + 3y

= (2 + 6) x^{2} â€“ (1 â€“ 5) xy + (6 â€“ 4) x â€“ (4 â€“ 3) y

= (8) x^{2} â€“ (- 4) xy + (2) x â€“ (1) y

= 8x^{2} + 4xy + 2x â€“ y

(iii) Given

x^{4} â€“ 6x^{3} + 2x â€“ 7 + 7x^{3} â€“ x + 5x^{2} + 2 â€“ x^{4}

Rearranging and collecting the like terms, we get:

= x^{4} – x^{4} â€“ 6x^{3} + 7x^{3} + 5x^{2} + 2x â€“ x â€“ 7 + 2

= (1 â€“ 1) x^{4} â€“ (6 â€“ 7) x^{3} + 5x^{2} + (2 â€“ 1) x – 7 + 2

= – (-1) x^{3} + 5x^{2} + (1) x â€“ 7 + 2

= x^{3} + 5x^{2} + x â€“ 5

**7. From the sum of 3x ^{2} â€“ 5x + 2 and -5x^{2} â€“ 8x + 6, subtract 4x^{2} â€“ 9x + 7.**

**Solution**

** **To find the sum

Add 3x^{2} â€“ 5x + 2 and -5x^{2} â€“ 8x + 6

(3x^{2} â€“ 5x + 2) + (-5x^{2} â€“ 8x + 6)

Rearranging and collecting the like terms, we get:

= 3x^{2} â€“ 5x^{2} â€“ 5x â€“ 8x + 2 + 6

= (3 â€“ 5) x^{2} â€“ (5 + 8) x + 2 + 6

= – 2x^{2 }â€“ 13x + 8

Now Subtract 4x^{2} â€“ 9x + 7 from -2x^{2 }– 13x + 8

Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = 4x^{2} â€“ 9x + 7

Changing the sign of each term of expression = – 4x^{2} + 9x â€“ 7

= – 2x^{2} â€“ 13x + 8 â€“ 4x^{2} + 9x â€“ 7

= -2x^{2} â€“ 13x + 8 – 4x^{2} â€“ 9x â€“ 7

= -2x^{2 }– 4x^{2 }â€“ 13x â€“ 9x + 8 â€“ 7

= (-2 – 4) x^{2 }â€“ (13 + 9) x + 8 â€“ 7

= – 6x^{2} â€“ 4x + 1

**8. If A = 7x ^{2} + 5xy â€“ 9y^{2}, B = – 4x^{2} + xy + 5y^{2} and C = 4y^{2} â€“ 3x^{2} â€“ 6xy then show that A + B + C = 0.**

**Solution**

Given

A = 7x^{2} + 5xy â€“ 9y^{2}

B = – 4x^{2} + xy + 5y^{2}

C = 4y^{2} â€“ 3x^{2} â€“ 6xy

To show A + B + C = 0

Substitute the value of A, B and C in A + B + C

A + B + C = (7x^{2} + 5xy â€“ 9y^{2}) + (- 4x^{2} + xy + 5y^{2}) + (4y^{2} â€“ 3x^{2} â€“ 6xy)

= 7x^{2} + 5xy â€“ 9y^{2} â€“ 4x^{2} + xy + 5y^{2} + 4y^{2} â€“ 3x^{2} â€“ 6xy

Rearranging and collecting the like terms, we get:

= 7x^{2} â€“ 4x^{2} â€“ 3x^{2} + 5xy + xy â€“ 6xy â€“ 9y^{2 }+ 5y^{2} + 4y^{2}

= (7 â€“ 4 â€“ 3) x^{2} + (5 + 1 â€“ 6) xy â€“ (9 â€“ 5 â€“ 4) y^{2}

= 0 x^{2} + 0 xy â€“ 0 y^{2}

^{ } = 0 + 0 + 0

= 0

Hence,

A + B + C = 0

**9. What must be added to 5x ^{3} â€“ 2x^{2} + 6x + 7 to make the sum x^{3} + 3x^{2} â€“ x + 1**

**Solution**

** **Let X be the expression to be added to 5x^{3} â€“ 2x^{2} + 6x + 7

(5x^{3} â€“ 2x^{2} + 6x + 7) + X = x^{3} + 3x^{2} â€“ x + 1

X = (x^{3} + 3x^{2} â€“ x + 1) â€“ (5x^{3} â€“ 2x^{2} + 6x + 7)

Changing the sign of each term of expression to be subtracted and add it to the expression from which subtraction is to be made

Term which is subtracted = 5x^{3} â€“ 2x^{2} + 6x + 7

Changing the sign of each term of expression = – 5x^{3 }+ 2x^{2} â€“ 6x â€“ 7

X = (x^{3} + 3x^{2} â€“ x + 1) + (- 5x^{3} + 2x^{2} â€“ 6x â€“ 7)

= x^{3} + 3x^{2} â€“ x + 1 – 5x^{3} + 2x^{2} – 6x – 7

Rearranging and collecting the like terms, we get:

= x^{3} – 5x^{3} + 3x^{2} + 2x^{2} â€“ x – 6x + 1 – 7

= (1 – 5) x^{3 }+ (3 + 2) x^{2} â€“ (1 + 6) x + 1 – 7

= – 4 x^{3} + 5 x^{2} + 7 x â€“ 6

âˆ´ – 4 x^{3} + 5 x^{2} + 7 x â€“ 6 must be added to 5x^{3} â€“ 2x^{2} + 6x + 7 to make the sum x^{3} + 3x^{2} â€“ x + 1