Selina Concise Class 6 Math Chapter 17 Fundamental Operations Exercise 17B Solution
EXERCISE 17B
(1) Find the sum of:
(i) (3a + 4b + 7c) + (- 5a + 3b – 6c) + (4a – 2b – 4c)
= 3a + 4b + 7c – 5a + 3b – 6c + 4a – 2b – 4c
= 3a + 4a – 5a + 4b + 3b – 2b + 7c – 6c – 4c
= 7a – 5a + 7b – 2b + 7c – 10c
= 2a + 5b – 3c
(ii) (2x2 + xy – y2) + (- x2 + 2xy + 3y2) + (3x2 – 10xy + 4y2)
= 2x2 + xy – y2 – x2 + 2xy + 3y2 + 3x2 – 10xy + 4y2
= 2x2 + 3x2 – x2 + xy + 2xy – 10xy + 3y2 + 4y2 – y2
= 5x2 – x2 + 3xy – 10xy + 7y2 – y2
= 4x2 – 7xy + 6y2
(iii) (x2 – x + 1) + (- 5x2 + 2x – 2) + (3x2 – 3x + 1)
= x2 – x + 1 – 5x2 + 2x – 2 + 3x2 – 3x + 1
= x2 + 3x2 – 5x2 – x – 3x + 2x + 1 + 1 – 2
= 4x2 – 5x2 – 4x + 2x + 2 – 2
= – x2 – 2x
(iv) a2 – ab + bc + 2ab + bc – 2a2 – 3bc + 3a2 + ab
= a2 + 3a2 – 2a2 – ab + 2ab + ab + bc + bc – 3bc
= 4a2 – 2a2 + 2ab + 2bc – 3bc
= 2a2 + 2ab – bc
(v) 4x2 + 7 – 3x + 4x – x2 + 8 – 10 + 5x – 2x2
= 4x2 – x2 – 2x2 – 3x + 4x + 5x + 7 + 8 – 10
= 4x2 – 3x2 – 3x + 9x + 15 – 10
= x2 + 6x + 5
(vi) 3x + 4xy – y2 + xy – 4x + 2y2 + 3y2 – xy + 6x
= 3x + 6x – 4x + 4xy + xy – xy – y2 + 2y2 + 3y2
= 9x – 4x + 5xy – xy – y2 + 5y2
= 5x + 4xy + 4y2
(2) Add the following expressions:
(i) – 17x2 – 2xy + 23y2 – 9y2 + 15x2 + 7xy + 13x2 + 3y2 – 4xy
= 15x2 + 13x2 – 17x2 – 2xy – 4xy + 7xy + 23y2 + 3y2 – 9y2
= 28x2 – 17x2 – 6xy + 7xy + 26y2 – 9y2
= 11x2 + xy + 17y2
(ii) – x2 – 3xy + 3y2 + 8 + 3x2 – 5y2 – 3 + 4xy + (- 6xy + 2x2 – 2 + y2)
= – x2 – 3xy + 3y2 + 8 + 3x2 – 5y2 – 3 + 4xy – 6xy + 2x2 – 2 + y2
= – x2 + 3x2 + 2x2 – 3xy + 4xy – 6xy + 3y2 – 5y2 + y2 + 8 – 3 – 2
= – x2 + 5x2 – 9xy + 4xy + 4y2 – 5y2 + 8 – 5
= 4x2 – 5xy – y2 + 3
(iii) a3 – 2b3 + a + b3 – 2a3 + b + (- 2b + 2b3 – 5a + 4a3)
= a3 – 2a3 + 4a3 – 2b3 + b3 + 2b3 + a – 5a + b – 2b
= 5a3 – 2a3 – 2b3 + 3b3 – 4a – b
= 3a3 + b3 – 4a – b
(3) Evaluate:
(i) 3a – (a + 2b)
= 3a – a – 2b
= 2a – 2b
(ii) (5x – 3y) – (x + y)
= 5x – 3y – x – y
= 4x – 4y
(iii) (8a + 15b) – (3b – 7a)
= 8a + 15b – 3b + 7a
= 15a + 12b
(iv) (8x + 7y) – (4y – 3x)
= 8x + 7y – 4y + 3x
= 11x + 3y
(v) 7 – (4a – 5)
= 7 – 4a + 5
= 2 – 4a
(vi) (6y – 13) – (4 – 7y)
= 6y – 13 – 4 + 7y
= 13y – 17
(4) Subtract:
(i) (a – 4b – 2c) – (5a – 3b + 2c)
= a – 4b – 2c – 5a + 3b – 2c
= a – 5a – 4b + 3b – 2c – 2c
= – 4a – b – 4c
(ii) 12x + 7y – 21z – (4x – 6y + 3z)
= 12x + 7y – 21z – 4x + 6y – 3z
= 12x – 4x + 7y + 6y – 21z – 3z
= 8x + 13y – 24z
(iii) 5a – 7b + 2c – (5 – a – 4b + 4c)
= 5a – 7b + 2c – 5 + a + 4b – 4c
= 5a + a – 7b + 4b + 2c – 4c
= 6a – 3b – 2c
(iv) x – y – z – (- 8x – 12y + 17z)
= x – y – z + 8x + 12y – 17z
= x + 8x – y + 12y – z – 17z
= 9x + 11y – 18z
(v) ab – 2cd + 2ac + bd – (2ab + cd – ac – 2bd)
= ab – 2cd + 2ac + bd – 2ab – cd + ac + 2bd
= ab – 2ab – 2cd – cd + 2ac + ac + bd + 2bd
= – ab – 3cd + 3ac + 3bd
(5) (i) bc – ca + ab – (- ab + bc – ca)
= bc – ca + ab + ab – bc + ca
= 2ab
(ii) 3x + 5y – 4z – (5x + 6y – 3z)
= 3x + 5y – 4z – 5x – 6y + 3z
= 3x – 5x + 5y – 6y – 4z + 3z
= – 2x – y – z
(iv) a2 + a + 1 – (1 – a + a2)
= a2 + a + 1 – 1 + a – a2
= 2a
(6) (i) 5x – 3x = 2x
(ii) 4x – (- x) = 4x + x = 5x
(iii) (2a + b) – (a – b)
= 2a + b – a + b
= a + 2b
(iv) 3x – (- 3x)
= 3x + 3x = 6x
(v) (2x + y) – (x – 2y)
= 2x + y – x + 2y
= x + 3y
(vi) a + b – 2c – (2a – b + c)
= a + b – 2c – 2a + b – c
= a – 2a + b + b – 2c – c
= – a + 2b – 3c
(7) (x + y – 2z + 2x – y + z) – (x + y + z)
= x + 2x + y – y – 2z + z – x – y – z
= 3x – x – y – 2z
(8) (3a – 2b + 4c + 3b – 2c) – (a – b – c)
= 3a + b + 2c – a + b + c
= 2a + 2b + 3c
(9) (3x – y + z + x + y – 3z) – (x – 2y – z)
= 4x – 2z – x + 2y + z
= 3x – z + 2y
(10) (x – 2z + x + y + z) – (x + y + x – z)
= 2x – z + y – (2x + y – z)
= 2x – z + y – 2x – y + z
= 0
(11) 3x – (x + 2y – 3z)
= 3x – x – 2y + 3z
= 2x – 2y + 3z
(12) 5x2 – 3y2 – (3x2 + 4xy – y2)
= 5x2 – 3y2 – 3x2 – 4xy + y2
= 2x2 – 2y2 – 4xy
(13) 3a2 + 2ab – b2 – (2a2 + 3b2)
= 3a2 + 2ab – b2 – 2a2 – 3b2
= a2 + 2ab – 4b2