eVidyarthi

Main Menu
  • eVidyarthi
  • School
    • Class 6th
      • Maths Class 6
      • Science Class 6
      • Hindi Class 6
      • व्याकरण
      • English Class 6
      • English Grammar
      • Sanskrit Class 6
      • Geography
      • Civics
      • History
    • Class 7th
      • Maths Class 7
      • Science Class 7
      • Hindi Class 7
      • व्याकरण
      • English Class 7
      • English Grammar
      • Sanskrit Class 7
      • Geography
      • Civics
      • History
    • Class 8th
      • Maths Class 8
      • Science Class 8
      • Hindi Class 8
      • व्याकरण
      • English Class 8
      • English Grammar
      • Sanskrit Class 8
      • Geography
      • Civics
      • History
    • Class 9th
      • Maths Class 9
      • Science Class 9
      • Hindi Class 9
      • English Class 9
      • English Grammar
      • व्याकरण
      • Economics Class 9
      • Geography Class 9
      • Civics Class 9
      • History Class 9
    • Class 10th
      • Maths Class 10
      • Science Class 10
      • Hindi Class 10
      • English Class 10
      • English Grammar
      • व्याकरण
      • Economics Class 10
      • History Class 10
      • Civics Class 10
      • Geography Class 10
    • Class 11th
      • Maths Class 11
      • Accounts Class 11
      • English Class 11
      • English Grammar
      • व्याकरण
      • Chemistry Class 11
      • Physics Class 11
      • Biology Class 11
    • Class 12th
      • Maths Class 12
      • Accounts Class 12
      • Chemistry Class 12
      • Physics Class 12
      • Biology Class 12
      • English Class 12
      • English Grammar
      • व्याकरण
    • Close
  • English
    • Basic English Grammar
    • Basic English Speaking
    • English Vocabulary
    • English Idioms & Phrases
    • Personality Enhancement
    • Interview Skills
    • Close
  • Softwares
    • Microsoft Word
    • PhotoShop
    • Excel
    • Illustrator
    • PowerPoint
    • Close
Maths Class 7 || Menu
  • Important
    • Sample Paper
    • Important Formulas
    • Revision Notes
    • Mathematics Book
    • MCQs
    • Close
  • Integers
    • Ex 1.1
    • Ex 1.2
    • Ex 1.3
    • Ex 1.4
    • MCQs
    • Ex. 1.1 NCERT Solutions
    • Ex. 1.2 NCERT Solutions
    • Ex. 1.3 NCERT Solutions
    • Ex. 1.4 NCERT Solutions
    • Close
  • Fractions and Decimals
    • Ex 2.1
    • Ex 2.2
    • Ex 2.3
    • Ex 2.4
    • Ex 2.5
    • Ex 2.6
    • Ex 2.7
    • MCQs
    • Ex. 2.1 NCERT Solutions
    • Ex. 2.2 NCERT Solutions
    • Ex. 2.3 NCERT Solutions
    • Ex. 2.4 NCERT Solutions
    • Ex. 2.5 NCERT Solutions
    • Ex. 2.6 NCERT Solutions
    • Ex. 2.7 NCERT Solutions
    • Close
  • Data Handling
    • Ex 3.1
    • Ex 3.2
    • Ex 3.3
    • Ex 3.4
    • MCQs
    • Ex. 3.1 NCERT Solutions
    • Ex. 3.2 NCERT Solutions
    • Ex. 3.3 NCERT Solutions
    • Ex. 3.4 NCERT Solutions
    • Close
  • Simple Equations
    • Ex 4.1
    • Ex 4.2
    • Ex 4.3
    • Ex 4.4
    • MCQs
    • Ex. 4.1 NCERT Solutions
    • Ex. 4.2 NCERT Solutions
    • Ex. 4.3 NCERT Solutions
    • Ex. 4.4 NCERT Solutions
    • Close
  • Lines and Angles
    • Ex 5.1
    • Ex 5.2
    • MCQs
    • Ex. 5.1 NCERT Solutions
    • Ex. 5.2 NCERT Solutions
    • Close
  • Triangle and its Properties
    • Ex 6.1
    • Ex 6.2
    • Ex 6.3
    • Ex 6.4
    • Ex 6.5
    • MCQs
    • Ex. 6.1 NCERT Solutions
    • Ex. 6.2 NCERT Solutions
    • Ex. 6.3 NCERT Solutions
    • Ex. 6.4 NCERT Solutions
    • Ex. 6.5 NCERT Solutions
    • Close
  • Congruence of Triangles
    • Ex 7.1
    • Ex 7.2
    • MCQs
    • Ex. 7.1 NCERT Solutions
    • Ex. 7.2 NCERT Solutions
    • Close
  • Comparing Quantities
    • Ex 8.1
    • Ex 8.2
    • Ex 8.3
    • MCQs
    • Ex. 8.1 NCERT Solutions
    • Ex. 8.2 NCERT Solutions
    • Ex. 8.3 NCERT Solutions
    • Close
  • Rational Numbers
    • Ex 9.1
    • Ex 9.2
    • MCQs
    • Ex. 9.1 NCERT Solutions
    • Ex. 9.2 NCERT Solutions
    • Close
  • Practical Geometry
    • Ex 10.1
    • Ex 10.2
    • Ex 10.3
    • Ex 10.4
    • Ex 10.5
    • MCQs
    • Ex. 10.1 NCERT Solutions
    • Ex. 10.2 NCERT Solutions
    • Ex. 10.3 NCERT Solutions
    • Ex. 10.4 NCERT Solutions
    • Ex. 10.5 NCERT Solutions
    • Close
  • Perimeter and Area
    • Ex 11.1
    • Ex 11.2
    • Ex 11.3
    • Ex 11.4
    • MCQs
    • Ex. 11.1 NCERT Solutions
    • Ex. 11.2 NCERT Soluions
    • Ex. 11.3 NCERT Solutions
    • Ex 11.4 NCERT Solutions
    • Close
  • Algebraic Expressions
    • Ex 12.1
    • Ex 12.2
    • Ex 12.3
    • Ex 12.4
    • MCQs
    • Ex. 12.1 NCERT Solutions
    • Ex. 12.2 NCERT Solutions
    • Ex. 12.3 NCERT Solutions
    • Ex. 12.4 NCERT Solutions
    • Close
  • Exponents & Powers
    • Ex 13.1
    • Ex 13.2
    • Ex 13.3
    • MCQs
    • Ex. 13.1 NCERT Solutions
    • Ex. 13.2 NCERT Solutions
    • Ex. 13.3 NCERT Solutions
    • Close
  • Symmetry
    • Ex 14.1
    • Ex 14.2
    • Ex 14.3
    • MCQs
    • Ex. 14.1 NCERT Solutions
    • Ex. 14.2 NCERT Solutions
    • Ex. 14.3 NCERT Solutions
    • Close
  • Visualising Solid Shapes
    • Ex 15.1
    • Ex 15.2
    • Ex 15.3
    • Ex 15.4
    • MCQs
    • Ex. 15.1 NCERT Solutions
    • Ex. 15.2 NCERT Solutions
    • Ex. 15.3 NCERT Solutions
    • Ex. 15.4 NCERT Solutions
    • Close

Class 7 Ex. 12.2 Maths NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.2

Ex 12.2 Class 7 Maths Question 1.
Simplify combining like terms:

(i) 21b -32 + 7b- 206

(ii) -z² + 13z² -5z + 7z³ – 15²

(iii) p – (p – q) – q – (q – p)

(iv) 3a – 2b — ab – (a – b + ab) + 3ab + 6 – a

(v) 5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² -3y²

(vi) (3y² + 5y – 4) – (8y – y² – 4)

Solution:

(i) 21b – 32 + 7b – 206
Re-arranging the like terms, we get
216 + 7b – 206 – 32
= (21 + 7 – 20)b – 32
= 8b – 32 which is required.

(ii) -z² + 13z² – 5z – 15z
Re-arranging the like terms, we get
7z³ – z² + 13z² – 5z + 5z – 15z
= 7z³ + (-1 + 13)z² + (-5 – 15)z
= 7z³ + 12z2 – 20z which is required.

(iii) p – (p – q) – q – (q – p)
=p – p + q – q – q + p
Re-arranging the like terms, we get

= p – q which is required.

(iv) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
= 3a – 2b – ab – a + b – ab + 3ab + b – a
Re-arranging the like terms, we get
= 3a – a – a – 2b + b + b – ab – ab + 3ab

= a + ab which is required.

(v) 5x² y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²
Re-arranging the like terms, we get
5x²y + 3x²y + 8xy² – 5x² + x² – 3y² – y² – 3y²
= 8x²y + 8xy² – 4x² – 7y² which is required.

(vi) (3y² + 5y – 4) – (8y – y² – 4)
= 3y² + 5y – 4 – 8y + y2 + 4 (Solving the brackets)
Re-arranging the like terms, we get
= 3y² + y² + 5y – 8y – 4 + 4
= 4y² – 3y which is required.

Ex 12.2 Class 7 Maths Question 2.
Add:

(i) 3mn, -5mn, 8mn, -4mn

(ii) t – 8tz, 3tz, -z, z – t

(iii) -7mn + 5, 12mn + 2, 9mn – 8, -2mn – 3

(iv) a + b – 3, b – a + 3, a – b + 3

(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy

(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5

(vii) 4x²y, -3xy², -5xy², 5x²y

(viii) 3p²q² – 4pq + 5, -10p²q², 15 + 9pq + 7p²q²

(ix) ab – 4a, 4b – ab, 4a – 4b

(x) x² – y² – 1, y² – 1 – x², 1 – x² – y²

Solution:

(i) 3mn, -5mn, 8mn, -4mn
= (3 mn) + (-5 mn) + (8 mn) + (- 4 mn)
= (3 – 5 + 8 – 4)mn
= 2mn which is required.

(ii) t – 8tz, 3tz – z, z – t
t – 8tz + 3tz – z + z – t
Re-arranging the like terms, we get
t – t – 8tz + 3tz – z + z
⇒ 0 – 5 tz + 0
⇒ -5tz which is required.

(iii) -7mn + 5, 12mn + 2, 9mn – 8, -2mn – 3
= -7mn + 5 + 12mn + 2 + 9mn – 8 + (-2mn) – 3
Re-arranging the like terms, we get
-7mn + 12 mn + 9mn – 2 mn + 5 + 2 – 8 – 3

= 12 mn – 4 which is required.

(iv) a + b – 3, b – a + 3, a – b + 3
⇒ a + b – 3 + b – a + 3 + a – b + 3
Re-arranging the like terms, we get
a – a + a + b + b – b – 3 + 3 + 3
⇒ a + b + 3 which is required.

(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
∴ 14x + 14y – 12xy – 13 + 18 – 7x – 10y + 8xy + 4xy
Re-arranging the like terms, we get
-12xy + 8xy + 4xy + 14x – 7x + 10y – 10y – 13 + 18

= 0 + 7x + 0 + 5
= 7x + 5 which is required

(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5 5m -In + 3n — 4m + 2 + 2m – 3mn – 5
Re-arranging the like terms, we get
5m – 4m + 2m – 7n + 3n- 3mn + 2 – 5
= 3m – 4n – 3mn – 3 which is required.

(vii) 4x²y, -3xy², -5xy², 5x²y
Re-arranging the like terms and adding, we get
4x²y – 5xy² – 3xy² + 5x²y
=9x²y — 8xy² which is required.

(viii) 3p²q² – 4pq + 5, -10p²q², 15 + 9pq + 7p²q²
= (3p²q² – 4pq + 5) + (-10p²q²) + (15 + 9pq + 7p²q²)
= 3p²q² – 4pq + 5 – 10p²q² + (15 + 9pq + 7p²q² )
= 3p²q² + 7p²q² – 10p²q² – 4pq + 9pq + 5 + 15
= 10p²q² – 10p²q² + 5pq + 20
= 0 + 5pq + 20
= 5pq + 20 which is required.

(ix) ab – 4a, 4b – ab, 4a – 4b
= ab – 4a + 4b – ab + 4a – 4b

= 0 + 0 + 0 = 0 which is required.

(x) x² – y² – 1, y² – 1 – x² , 1 – x² – y²
= x² – y² – 1 + y² – 1 – x² + 1 – x² – y²

= -x² – y² – 1
= -(x² + y² + 1) which is required.

Ex 12.2 Class 7 Maths Question 3.
Subtract:

(i) -5y² from y²

(ii) 6xy from -12xy

(iii) (a – b) from (a + b)

(iv) a(b – 5) from b(5 – a)

(v) -m² + 5mn from 4m² – 3mn + 8

(vi) -x² + 10x – 5 from 5x – 10

(vii) 5a² – 7ab + 5b² from 3ab – 2a² – 2b²

(viii) 4pq – 5q² – 3p² from 5p² + 3q² – pq

Solution:

(i) -5y² from y² = y² – (-5y²)
= y² + 5y² = 6y²

(ii) 6ry from -12ry = -12xy – 6xy = -18xy which is required.
(iii) (a – b) from (a + b)
= (a + b) – (a – b)
= a + b – a + b = 2b which is required

(iv) a(b – 5) from b(5 – a)
= b(5 – a) – a(b – 5)
= 5b – ab – ab + 5a
= 5a – 2ab + 5b
= 5a + 5b – 2ab which is required.

(v) -m² + 5mn from 4m2 – 3mn + 8
= (4m² – 3mn + 8) – (-m² + 5mn)
= 4m² – 3mn + 8 + m² – 5mn
= 4m² + m2 – 3mn – 5mn + 8
= 5m² – 8mn + 8 which is required.

(vi) -x² + 10x – 5 from 5x – 10
= (5x – 10) – (-x² + 10x – 5)
= 5x – 10 + x² – 10x + 5
= x² + 5x – 10x – 10 + 5
= x² – 5x – 5 which is required.

(vii) 5a² – 7ab + 5b² from 3ab – 2a² – 2b²
= (3ab – 2a² – 2b²) – (5a² – 7ab + 5b²)
= 3ab – 2a² – 2b² – 5a² + 7ab – 5b²
= 3ab + 7ab – 2a² – 5a² – 2b² – 5b²
= 10ab – 7a² – 7b²
which is required.

(viii) 4pq – 5q² – 3p² from 5p² + 3q² – pq
= (5p² + 3q² – pq) – (4pq – 5q² – 3p²)
= 5p² + 3q² – pq – 4pq + 5q² + 3p²
= 5p² + 3p² + 3q² + 5q² – pq – 4pq
= 8p² + 8q² – 5pq
which is required.

Ex 12.2 Class 7 Maths Question 4.
(a) What should be added to x² + xy + y²to obtain 2x² + 3xy?
(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?

Solution:

(a) (2x² + 3xy) – (x² + xy + y²)
= 2x² + 3xy – x² – xy – y²
= 2x² – x² + 3xy – xy – y²
= x² + 2xy – y2 is required expression.

(b) (2a + 8b + 10) – (-3a + 7b + 16)
= 2a + 8b + 10 + 3a – 7b – 16
= 2a + 3a + 8b – 7b + 10 – 16
= 5a + b – 6 is required expression.

Ex 12.2 Class 7 Maths Question 5.
What should be taken away from 3x² – 4y² + 5xy + 20 to obtain -x² – y² + 6xy + 20?

Solution:

Let A be taken away.
∴ (3x² – 4y² + 5 xy + 20)-A
= -x² – y² + 6xy + 20
⇒ A = (3x² – 4y² + 5xy + 20) – (-x²2 – y² + 6xy + 20)
= 3x² – 4y² + 5xy + 20 + x² + y² – 6xy – 20
= 3x² + x² – 4y² + y² + 5xy – 6xy + 20 – 20
= 4x² – 3y2 – xy is required expression.

Ex 12.2 Class 7 Maths Question 6.
(a) From the sum of 3x – y + 11 and -y – 11, subtract 3x – y – 11.
(b) From the sum of 4 + 3x and 5 – 4x + 2×2, subtract the sum of 3x² – 5x and -x² + 2x + 5.

Solution:

(a) Sum of 3x – y + 11 and -y – 11
= (3x – y + 11) + (-y – 11)
= 3x – y + 11 – y – 11
∴ 3x – 2y – (3x – 2y) – (3x – y – 11)
= 3x – 2y – 3x + y + 11
= 3x – 3x – 2y + y + 11
= -y + 11 is required solution.

(b) Sum of (4 + 3x) and (5 – 4x + 2x²)
= 4 + 3x + 5 – 4x + 2×2
= 2x² – 4x + 3x + 9 = 2x² – x + 9
Sum of (3x² – 5x) and (-x² + 2x + 5)
= (3x² – 5x) + (-x² + 2x + 5)
= 3x² – 5x – x² + 2x + 5 = 2x² – 3x + 5
Now (2x² – x + 9) – (2x² – 3x + 5)
= 2x² – x + 9 – 2x² + 3x – 5
= 2x² – 2x² + 3x – x + 4
= 2x + 4 is required expression.

 

Android App

eVidyarthi

Search On eVidyarthi

Evidyarthi on Facebook

Like us on Facebook

Follow Evidyarthi on Youtube

Learn English
Learn English Through हिन्दी
Job Interview Skills
English Grammar
हिंदी व्याकरण - Vyakaran
Mathematics Class 6th
Science Class 6th
हिन्दी Class 6th
Mathematics Class 7th
Science Class 7th
हिन्दी Class 7th
Mathematics Class 8th
Science Class 8th
हिन्दी Class 8th
Mathematics Class 9th
English Class 9th
Science Class 9th
Mathematics Class 10th
English Class 10th
Mathematics Class XI
Chemistry Class XI
Accountancy Class 11th
Accountancy Class 12th
Mathematics Class 12th
Microsoft Word
Microsoft Excel
Microsoft PowerPoint
Adobe PhotoShop
Adobe Illustrator
Learn German
Learn French
IIT JEE
Privacy Policies, Contact Us
Copyright © 2020 eVidyarthi and its licensors. All Rights Reserved.