Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12E Goyal Brothers ICSE Maths Solutions Ch-12. We provide step by step Solutions of Addition in 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-12E 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-12E | Addition in Algebraic Expression |
| Academic Session | 2024 – 2025 |
Addition in Algebraic Expression
There are two methods to add and subtract algebraic expressions, namely the horizontal method and the vertical 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
- the given expression must be written column-wise one below the other.
- For adding two or more algebraic expressions the like terms of both the expressions are grouped together.
- The coefficients of like terms are added together using simple addition techniques
- variable which is common is retained as it is.
- unlike terms are retained as it is
- result obtained is the addition of two or more algebraic expressions
Exercise- 12E
( Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12E Goyal Brothers ICSE Maths Solutions Ch-12)
Que-1: Add :
(i) 9x,7x (ii) 13p,6p,2p (iii) 8xy,7xy,xy (iv) 5y,-13y (v) 4x²,-9x² (vi) 3a²b,-5a²b (vii) (1/2)mn,2mn (viii) (1/3)x²y,3x²y (ix) 5ab²,-ab²
Sol: (i) 9x+7x
= 16x
(ii) 13p+6p+2p
= 21p
(iii) 8xy+7xy+xy
= 16xy
(iv) 5y+(-13y)
= -8y
(v) 4x²+(-9x)²
= -5x²
(vi) 3a²b+(-5a²b)
= -2a²b
(vii) (1/2)mn + 2mn
– (1/2+2)mn
= 5/2 mn
(viii) (1/3)x²y + 3x²y
= (1/3+3)x²y
= 10/3 x²y
(ix) 5ab²+(-ab²)
= 4ab²
Que-2: Add :
(i) 5a,-3a,4a (ii) -2b,b,-3b (iii) 4ab,-5ab,-3ab (iv) 6xy²,-8xy²,-3xy² (v) 4m²n,-m²n,-6m²n (vi) 2xyz,-5xyz,-xyz
Sol: (i) 5a+(-3a)+4a = 6a
(ii) -2b+b+(-3b) = -4b
(iii) 4ab+(-5ab)+(-3ab) = -4ab
(iv) 6xy²+(-8xy²)+(-3xy²) = -5xy²
(v) 4m²n+(-m²n)+(-6m²n) = 3m²n
(vi) 2xyz+(-xyz)+(-5xyz) = -4xyz
Que-3: Add :
(i) -6x,-9x (ii) -3y,-y,-7y (iii) -8xy,-4xy,6xy (iv) 7m²n,-2m²n,-3m²n (v) -2ab²,-8ab²,5ab² (vi) (1/2)yz,2yz,-yz (vii) 5a³,-3a³,(-1/2)a³ (viii) (-1/2)a²,(-1/3)a²,2a²
Solution- (i) -6x+(-9x) = -15x
(ii) -3y+(-y)+(-7y) = -11y
(iii) -8xy+(-4xy)+6xy = -6xy
(iv) 7m²n+(-2m²n)+(-3m²n) = 2m²n
(v) -2ab²+(-8ab²)+5ab² = -5ab²
(vi) (1yz/2)+2yz+(-yz)
= (1/2+1)yz = (3/2)yz
(vii) 5a³+(-3a³)+(-1/2)a³
= (2-1/2)a³ = (3/2)a³
(viii) (-1a²/2)+(-1a²/3)+2a²
= ((-1/2)-(1/3)+2)a²
= (7/6)a²
Find the sum of the following algebraic expressions :
( Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12E Goyal Brothers ICSE Maths Solutions Ch-12)
Que-4: 8a-3b+11c, 5b-6a+7c and 9c+2a-8b
Sol: Given expressions are
8a-3b+11c, 5b-6a+7c and 9c+2a-8b
= (8a – 3b + 11c) + (5b – 6a + 7c) + (9c + 2a – 8b)
= (8a – 6a + 2a) + (- 3b + 5b – 8b) + (11c + 7c + 9c)
[∵ grouping like terms]
= (10a – 6a) + (5b – 11b) + (18c + 9c)
= 4a – 6b + 27c
Que-5: 3y+4z-6x, 2x-4y+z and 5z-8y-x
Sol: (3y+4z-6x)+(2x-4y+z)+(5z-8y-x)
3y+4z-6x+2x-4y+z+5z-8y-x
-9y+10z-5x
Que-6: 8x-5y+3z, 6y-11x-z, 7y-2z and x-2y
Sol: = 8x-11x+x-5y+6y+7y-2y+3z-2z-z
= -2x+6y+3z-3z
= -2x+6y
Que-7: 10x²+8x-7, 3x-13x²+5 and 9-6x-5x²
Sol: 10x² + 8x – 7 + 3x – 13x² + 9 – 5x + 6 + x²
= -8x²+5x-7
Que-8: 5x³-8x²+6x-3, x²-2x+15 and 16-2x³
Sol: 5x³-8x²+6x-3+x²-2x+15+16-2x³
= 3x³-7x²+4x+28
Que-9: 3x²-(1x/5)+(7/3), (-1x²/4)+(1x/3)-(1/6) and -2x²-(1x/2)+(1/5)
Sol: 3x²-(1x/5)+(7/3) + (-1x²/4)+(1x/3)-(1/6) + [-2x²-(1x/2)+(1/5)]
= 3x²-(1x²/4)-2x²-(1x/5)+(1x/3)-(1x/2)+(7/3)-(1/6)+(1/5)
= [(12-1-8)/4x²][(-6x+10x-15x)/30]+[(70-5+6)/30]
= (3x²/4)-(11x/30)+(71/30)
Que-10: 2a²-3ab+4bc, 6ab-a²-5bc and 13bc-8a²+ab
Sol: 2a²-3ab+4bc-a²+6ab-5bc-8a²+ab+13bc
= 2a²-a²-8a²-3ab+6ab+ab+4bc-5bc+13bc
= -7a²+4ab+12bc
Que-11: 6x²+2xy-y², xy-x²-2y² and 5y²-8x²+3xy
Sol: 6x²-x²-8x²-y²-2y²+5y²+2xy+xy+3xy
= -3x²+2y²+6xy
Que-12: 2x²-3y²+6z², y²-2x²+z², z²-6x²-8y² and x²-y²
Sol: 2x²-2x²-6x²+x²-3y²+y²-8y²-y²+6z²+z²+z²
= -5x²-11y²+8z²
Que-13: 6m²n+3mn-2n², n²-mn-m²n and mn-3n²-4m²n
Sol: 6m²n-m²n-4m²n-2n²+n²-3n²+3mn-mn+mn
= m²n-4n²+3mn
Que-14: Simplify :
(i) 2m³-5m²+3m-6-5m³+2m²-8m+2+6m+5
(ii) 2x⁴-5x³+2x-5+6x³-3x+7-x⁴-2x³+2
(iii) 3p²-2pq+5p-4q+5pq-3p+4p²+3q
Sol: (i) 2m³-5m²+3m-6-5m³+2m²-8m+2+6m+5
= 2m³-5m³-5m²+2m²+3m-8m+6m+5+2-6
= -3m³-3m²+m+1
(ii) 2x⁴-5x³+2x-5+6x³-3x+7-x⁴-2x³+2
= 2x⁴-x⁴-5x³+6x³-2x³+2x-3x-5+7+2
= x⁴-x³-x+4
(iii) 3p²-2pq+5p-4q+5pq-3p+4p²+3q
= 3p²+4p²-2pq+5pq+5p-3p-4q+3q
= 7p²+3pq+2p-q
— end of Fundamental Concepts of Algebra Class 6 RS Aggarwal Exe-12E Goyal Brothers ICSE Solutions :–
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