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 -7m²n (viii) (1b/2) from -2b (ix) (-1c/3) from 3c
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)
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 :–
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