Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12F Goyal Brothers ICSE Maths Solutions Ch-12. We provide step by step Solutions of **Subtraction of Algebraic Expression** for ICSE Class-6 Foundation RS Aggarwal of Goyal Brothers Prakashan . Visit official Website **CISCE** for detail information about ICSE Board Class-6 Mathematics.

**Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12F Goyal Brothers ICSE Maths Solutions Ch-12**

Board | ICSE |

Subject | Maths |

Class | 6th |

Ch-12 | Fundamental Concepts of Algebra |

Writer | RS Aggrawal |

Book Name | Foundation |

Exe-12F | Subtraction of Algebraic Expression |

Academic Session | 2024 – 2025 |

**Subtraction of Algebraic Expression**

subtract algebraic expressions in two methods. Horizontal Method, Column Method:

**Horizontal Method:**

- Write the given algebraic expressions using an additional symbol.
- Open the brackets and multiply the signs
- Now, combine the like terms
- Add the coefficients. Keep the variables and exponents on the variables the same

**Column Method:**

- write the expressions to be subtracted below the expression from which it is to be subtracted.
- Like terms are placed below each other.
- The sign of each term which is to be subtracted is reversed and then the resulting expression is added normally.

**Exercise- 12F**

( Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12F **Subtraction of Algebraic Expression **Goyal Brothers ICSE Maths Solutions Ch-12 )

**Que-1: Subtract :**

(i) 8x from 15x (ii) 3ab² from 7ab² (iii) 5b from -b (iv) -4x from 11x (v) -x from x (vi) 2ab from -2ab (vii) -3m²n from -7m**²n (viii) (1b/2) from -2b (ix) (-1c/3) from 3c**

(i) 8x from 15x (ii) 3ab² from 7ab² (iii) 5b from -b (iv) -4x from 11x (v) -x from x (vi) 2ab from -2ab (vii) -3m²n from -7m

**Sol: **(i) 15x-8x = 7x

(ii) 7ab²-3ab² = 4ab²

(iii) -b-5b = -6b

(iv) 11x-(-4x) = 15x

(v) x-(-x) = 2x

(vi) -2ab-2ab = -4ab

(vii) -7m²n-(-3m²n) = -4m²n

(viii) -2b-(1b/2)

= (-4b-b)/2 = -5b/2

(ix) 3c-(-1c/3)

= (9c+1c)/3 = 10c/3

**Que-2: Subtract :**

(i) a+2b-c from 3a-b+2c (ii) -3a+b+6c from 5a-3b-4c (iii) 2m-3n+p from -m+n-2p (iv) -6x-9y+15z from x-y-3z (v) (-1p/2)+q-r from (1p/2)-(1q/3)-(3r/2)

(i) a+2b-c from 3a-b+2c (ii) -3a+b+6c from 5a-3b-4c (iii) 2m-3n+p from -m+n-2p (iv) -6x-9y+15z from x-y-3z (v) (-1p/2)+q-r from (1p/2)-(1q/3)-(3r/2)

**Sol: **(i) (3a-b+2c)-(a+2b-c)

= 3a-b+2c-a-2b+c

= 2a-3b+3c

(ii) (5a-3b-4c)-(-3a+b+6c)

= 5a-3b-4c+3a-b-6c

= 8a-4b-10c

(iii) (-m+n-2p)-(2m-3n+p)

= -m+n-2p-2m+3n-p

= -3m+4n-3p

(iv) (x-y-3z)-(-6x-9y+15z)

= x-y-3z+6x+9y-15z

= 7x+8y-18z

(v) [(1p/2)-(1q/3)-(3r/2)]-[(-1p/2)+q-r]

= (1p/2)-(1q/3)-(3r/2)+(1p/2)-q+r

= (1p/2)+(1p/2)-(1q/3)-q-(3r/2)+r

= [(1p+1p)/2]-[(q+3q)/3]-[(3r-2r)/2]

= (2p/2)-(4q/3)-(1r/2)

= p-(4q/3)-(1r/2).

**Que-3: Subtract :**

(i) 3x²-5x+6 from 5x²-x-3

(ii) 2x²+3x-1 from x²+x-5

(iii) 1-x+x² from x²+x-1

(iv) a²+a-1 from a-a²

(v) 6y²-y-8 from -y²+2y+7

**Sol: **(i) 5x²-x-3 – (3x²-5x+6)

= 5x²-x-3-3x²+5x-6

= 2x²+4x-9

(ii) x²+x-5 – (2x²+3x-1)

= x²+x-5-2x²-3x+1

= -x²-2x-4

(iii) x²+x-1 – (1-x+x²)

= x²+x-1-1+x-x²

= 2x-2

(iv) a-a² – (a²+a-1)

= a-a²-a²-a+1

= -2a²+1

(v) -y²+2y+7 – (6y²-y-8)

= -y²+2y+7-6y²+y+8

= -7y²+3y+15

**Que-4: Subtract :**

(i) p²-2pq+q² from p²+2pq-q²

(ii) x²-2xy+y² from 5xy-2x²-3y²

(iii) 5xy-3x²-2y²-3 from x²-2xy+6y²+8

(iv) 6x³-8x²+4x-2 from 5-4x+6x²-8x³

**Sol: **(i) p²+2pq-q² – (p²-2pq+q²)

= p²+2pq-q²-p²+2pq-q²

= 4pq-2q²

(ii) 5xy-2x²-3y² – (x²-2xy+y²)

= 5xy-2x²-3y²-x²+2xy-y²

= -3x²-4y²+7xy

(iii) x²-2xy+6y²+8 – (5xy-3x²-2y²-3)

= x²-2xy+6y²+8-5xy+3x²+2y²+3

= 4x²+8y²-7xy+11

(iv) 5-4x+6x²-8x³ – (6x³-8x²+4x-2)

= 5-4x+6x²-8x³-6x³+8x²-4x+2

= -14x³+14x²-8x+7.

**Qu-5: How much is a+2b greater than b-a ?**

**Sol: **It is given that, a + 2b > b – a

It is needed to find by how much a + 2b is greater than b – a

Provided that a + 2b ; b – a, then a + 2b is surely greater than b – a

Then let’s consider, a + 2b**
**⇒ a + 2b

Subtracting b – a from a + 2b, we get:

⇒ (a + 2b) – (b – a)

⇒ 2a + b

**Que-6: How much is a-2b+3c greater than 2a+3b-c ?**

**Sol: ** Term to be subtracted = 2a + 3b – c

Changing the sign of each term of the expression gives -2a – 3b + c.

On adding:

(a – 2b + 3c )+(-2a – 3b + c. )

= a – 2b + 3c -2a – 3b + c.

= (1-2)a – (2+3)b +(3+1)c

= -a – 5b + 4c

**Que-7: How much does 3x²-4x+3 exceed x³-x²+2x-1 ?**

**Sol: **3x²-4x+3 – (x³-x²+2x-1)

= 3x²-4x+3-x³+x²-2x+1

= -x³+4x²-6x+4

**Que-8: How much is p-2q+3r less than 3r+5 ?**

**Sol: **Given two expressions are

p-2q+3r, 3r + 5

3r+5 – ( p-2q+3r )

= 3r+5-p+2q-3r

= 5 – p + 2q

**Que-9: What must be subtracted from 3x to get 5x+1 ?**

**Sol: **Let the expression to be subtracted be ‘A’.

3x – A = 5x+1

A = 3x-5x-1

A = -2x-1

**Que-10: What must be subtracted from 2x+3y to get y-3x ?**

**Sol: **Let the expression to be subtracted be ‘A’.

2x+3y – A = y-3x

A = 2x+3y-y+3x

A = 5x+2y

**Que-11: What must be subtracted from x²+2x-3 to get 2x²-4 ?**

**Sol: **Let the expression to be subtracted be ‘A’.

x² + 2x – 3 – A = 2x² – 4

A = x² + 2x – 3 – (2x² – 4)

Re-arranging the terms,

A = x² – 2x² + 2x – 3 + 4

A = -x² + 2x + 1

**Que-12: What must be added to 6x to get 4x+1 ?**

**Sol: **Let the added expression be y

y+6x = 4x+1

y = 4x+1-6x

y = -2x+1

**Que-13: What must be added to a+2b to get b-2a ?**

**Sol: **Let the added expression be x

x+a+2b = b-2a

x = b-2a-a-2b

x = -3a-b

**Que-14: What must be added to 5x²+6x-3 to get 3x+2 ?**

**Sol: **Let the expression to be added be ‘A’.

5x²+6x-3 + A = 3x+2

A = 3x+2-5x²-6x+3

A = -5x²-3x+5

**Que-15: Subtract 5x²-8x+6 from the sum of 3x²-4x+2 and 7-5x²-6x.**

**Sol: **the sum of 3x²- 4x + 2 and 7 – 5x² – 6x.

= 3x²- 4x + 2 + (7 – 5x² – 6x)

= 3x²– 5x² – 4x – 6x + 2 + 7

= -2x² – 10x +9

Subtract 5x²-8x+6 from -2x²-10x+9

= -2x²-10x+9 – (5x²-8x+6)

= -2x²-10x+9-5x²+8x-6

= -7x²-2x+3

**Que-16: Subtract 3y²-5y-4 from the sum of y-5y²+1 and 3y+4y²-5.**

**Sol: **the sum of y-5y²+1 and 3y+4y²-5

= y-5y²+1+3y+4y²-5

= -y²+4y-4

Subtract 3y²-5y-4 from -y²+4y-4

= -y²+4y-4 – (3y²-5y-4)

= -y²+4y-4-3y²+5y+4

= -4y²+9y

–: End of Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12F Subtraction of Algebraic Expression :–

**Return to :- ICSE Class -6 RS Aggarwal Goyal Brothers Math Solutions**

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