Selina Concise Class 7 Math Chapter 11 Fundamental Concepts Exercise 11B Solution
EXERCISE 11B
(1) Fill in the blanks:
(i) 8x + 5x = 13x
(ii) 8x – 5x = 3x
(iii) 6xy2 + 9xy2 = 15xy2
(iv) 6xy2 – 9xy2 = – 3xy2
(v) 8a + 6a + 5b = 14a + 5b
(vi) 5 + 7xy + 6 + 3xy = 11 + 10xy
(vii) 4a + 3b – 7a + 4b = – 3a + 7b
(viii) – 15x + 13x + 8 = – 2x + 8
(ix) 6x2y + 13xy2 – 4x2y + 2xy2
= 2x2y + 15xy2
(x) 16x2 – 9x2 = 7x2 and 25xy2 – 17xy2 = 8xy2.
(2) Add:
(i) – 9x + 3x + 4x
= – 9x + 7x = – 2x
(ii) 23y2 + 8y2 + (- 12y2)
= 31y2 – 12y2
= 19y2
(iii) 18pq + (- 15pq) + 3pq
= 18pq + 3pq – 15pq
= 21pq – 15pq
= 6pq
(3) Simplify:
(i) 3m + 12 m – 5m
= 15m – 5m
= 10m
(ii) 7n2 – 9n2 + 3n2
= 7n2 + 3n2 – 9n2
= 10n2 – 9n2
= n2
(iii) 25zy – 8zy – 6zy
= 25zy – 14zy
= 11zy
(iv) – 5ax2 + 7ax2 – 12ax2
= – 17ax2 + 7ax2
= – 10ax2
(v) – 16am + 4mx + 4am – 15mx + 5am
= – 16am + 4am + 5am + 4mx – 15mx
= – 16am + 9am – 11mx
= – 7am – 11mx
(4) Add:
(i) a + b + (2a + 3b)
= a + b + 2a + 3b
= 3a + 4b
(ii) 2x + y + (3x – 4y)
= 2x + y + 3x – 4y
= 5x – 3y
(iii) – 3a + 2b + (3a + b)
= – 3a + 2b + 3a + b
= 3b
(iv) 4 + x + (5 – 2x + 6x)
= 4 +x + 5 – 2x + 6x
= 9 + 7x – 2x
= 9 + 5x
(5) Find the sum of:
(i) 3x + 8y + 7z + 6y + 4z – 2x + 3y – 4x + 6z
= 3x – 2x – 4x + 8y + 6y + 3y + 7z + 4z + 6z
= 3x – 6x + 17y + 17z
= – 3x + 17y + 17z
(ii) 3a + 5b + 2c + 2a + 3b – c + a + b + c
= 3a + 2a + a + 5b + 3b + b + 2c – c + c
= 6a + 9b + 2c
(iii) 4x2 + 8xy – 2y2 + 8xy – 5y2 + x2
= 4x2 + x2 + 8xy + 8xy – 2y2 – 5y2
= 5x2 + 16xy – 7y2
(iv) 9x2 – 6x + 7 + 5 – 4x + 6 – 3x2
= 9x2 – 3x2 – 6x – 4x + 7 + 5 + 6
= 6x2 – 10x + 18
(v) 5x2 – 2xy + 3y2 + (- 2x2 + 5xy + 9y2) + (3x2 – xy – 4y2)
= 5x2 – 2xy + 3y2 – 2x2 + 5xy + 9y2 + 3x2 – xy – 4y2
= 5x2 – 2x2 + 3x2 – 2xy + 5xy – xy + 3y2 + 9y2 – 4y2
= 8x2 – 2x2 + 5xy – 3xy + 12y2 – 4y2
= 6x2 + 2xy + 8y2
(vi) a2 + b2 + 2ab + 2b2 + c2 + 2bc + 4c2 – a2 + 2ac
= a2 – a2 + b2 + 2b2 + c2 + 4c2 + 2ab + 2bc + 2ac
= 3b2 + 5c2 + 2ab + 2bc + 2ac
(vii) 9ax – 6bx + 8 + 4ax + 8bx – 7 – 6ax – 4bx – 3
= 9ax + 4ax – 6ax – 6bx + 8bx – 4bx + 8 – 7 – 3
= 13ax – 6ax – 10bx + 8bx + 8 – 10
= 7ax – 2bx – 2
(viii) abc + 2ba + 3ac + 4ca – 4ab + 2bca + 2ab – 3abc – 6ac
= abc + 2bca – 3abc + 2ba – 4ab + 2ab + 3ac + 4ca – 6ac
= 3abc – 3abc + 4ab – 4ab + 7ac – 6ac
= ac
(ix) 4a2 + 5b2 – 6ab + 3ab + 6a2 – 2b2 + 4b2 – 5ab
= 4a2 + 6a2 + 5b2 – 2b2 + 4b2 – 6ab + 3ab – 5ab
= 10a2 + 3b2 + 4b2 – 11ab + 3ab
= 10a2 + 7b2 – 8ab
(x) x2 + x – 2 + 2x – 3x2 + 5 + 2x2 – 5x + 7
= x2 + 2x2 – 3x2 + x + 2x – 5x – 2 + 5 + 7
= 3x2 – 3x2 + 3x – 5x – 2 + 12
= 10 – 2x
(xi) 4x3 + 2x2 – x + 1 + 2x3 – 5x2 – 3x + 6 + x2 + 8 + 5x3 – 7x
= 4x3 + 2x3 + 5x3 + 2x2 – 5x2 + x2 – x – 3x – 7x + 1 + 6 + 8
= 11x3 + 3x2 – 5x2 – 11x + 15
= 11x3 – 2x2 – 11x + 15
(6) Find the sum of:
(i) x + 3y
(ii) – 2a + 5
= 5 – 2a
(iii) – 4x2 + 7x
= 7x – 4x2
(iv) 4a + (- 7b)
= 4a – 7b
(v) x3 + 3x2y + 2y2
(vi) 11 + (- by)
= 11 – by
(7) Perimeter = 2x + 3y + x + 5y + 7x – 2y
= 2x + x + 7x + 3y + 5y – 2y
= 10x + 8y – 2y
= 10x + 6y
(8) Perimeter of rectangle = 2 (6a + 9b + 8a – 4b)
= 2 × (14a + 5b)
= (2 × 14a) + (2 × 5b)
= 28a + 10b
(9) Subtract the second expression from the first:
(i) (2a + b) – (a + b)
= 2a + b – a – b
= a
(ii) – 2b + 2c – (b + 3c)
= – 2b + 2c – b – 3c
= – 3b – c
(iii) 5a + b – (- 6b + 2a)
= 5a + b + 6b – 2a
= 3a + 7b
(iv) a3 – 1 + a – (3a – 2a2)
= a3 – 1 + a – 3a – 2a2
= a3 – 1 – 2a – 2a2
(v) p + 2 – 1
= p + 1
(vi) x + 2y + z – (- x – y – 3z)
= x + 2y + z + x + y + 3z
= 2x + 3y + 4z
(vii) 3a2 – 8ab – 2b2 – (3a2 – 4ab + 6b2)
= 3a2 – 8ab – 2b2 – 3a2 + 4ab – 6b2
= 3a2 – 3a2 – 8ab + 4ab – 2b2 – 6b2
= – 4ab – 8b2
(viii) 4pq – 6p2 – 2q2 – 9p2
= 4pq – 6p2 – 9p2 – 2q2
= 4pq – 15p2 – 2q2
(ix) 10abc – (2a2 + 2abc – 4b2)
= 10abc – 2a2 – 2abc + 4b2
= 10abc – 2abc – 2a2 + 4b2
= 8abc – 2a2 + 4b2
(x) a2 + ab + c2 – (a2 – d2)
= a2 + ab + c2 – a2 + d2
= ab + c2 + d2
(10) SDubtract:
(i) (8 – x) – 4x
= 8 – x – 4x
= 8 – 5x
(ii) c + 3d – (- 8c)
= c + 3d + 8c
= 9c + 3d
(iii) b + 6c – (- 5a – 2b)
= b + 6c + 5a + 2b
= 3b + 6c + 5a
(iv) 3p2 – 8p – (4p + p2)
= 3p2 – 8p – 4p – p2
= 2p2 – 12p
(v) 4a – b – 2c – (5a – 3b + 2c)
= 4a – b – 2c – 5a + 3b – 2c
= 4a – 5a – b + 3b – 2c – 2c
= – a + 2b – 4c
(vi) xy – yz + xz – (- xy + yz – zx)
= xy – yz + xz + xy – yz + zx
= 2xy – 2yz + 2xz
(vii) 3x2 – 5xy + 3y2 – (2x2 – 7xy – y2)
= 3x2 – 5xy + 3y2 – 2x2 + 7xy + y2
= x2 + 2xy + 4y2
(viii) 2b2 – a2 + 2ab – (a2 – 3ab – 6b2)
= 2b2 – a2 + 2ab – a2 + 3ab + 6b2
= 2b2 + 6b2 – a2 – a2 + 2ab + 3ab
= 8b2 – 2a2 + 5ab
(ix) – 3y2 + 5xy2 – 7x2 – 9x2y – (4x2 – 5x2y + y2)
= – 3y2 + 5xy2 – 7x2 – 9x2y – 4x2 – 5x2y – y2
= – 3y2 – y2 + 5xy2 – 9x2y – 5x2y – 7x2 – 4x2
= – 4y2 + 5xy2 – 14x2y – 11x2
(x) 3m3 + 4 – (6m3 + 4m2 + 7m – 3)
= 3m3 + 4 – 6m3 – 4m2 – 7m + 3
= – 3m3 + 7 – 4m2 – 7m
(11) (4a2 + 3 – 8a + 9a – 7) – (- 5a2 – 3a + 1)
= 4a2 + 3 – 8a + 9a – 7 + 5a2 + 3a – 1
= 4a2 + 5a2 + 3 – 7 – 1 – 8a + 9a + 3a
= 9a2 + 3 – 8 – 8a + 12a
= 9a2 – 5 + 4a
(12) (8x3 – 6x2 + 9x – 10) – (4x3 + 2x2 + 7x – 3)
= 8x3 – 6x2 + 9x – 10 – 4x3 – 2x2 – 7x + 3
= 8x3 – 4x3 – 6x2 – 2x2 + 9x – 7x – 10 + 3
= 4x3 – 8x2 + 2x – 7
(13) a2 – a – a3 + 1 – (2a3 + 5a – a2 – 6)
= a2 – a – a3 + 1 – 2a3 – 5a + a2 + 6
= a2 + a2 – a – 5a – a3 – 2a3 + 1 + 6
= 2a2 – 6a – 3a3 + 7
(14) a2 + b2 + 2ab – (- 4ab + 2b2)
= a2 + b2 + 2ab + 4ab – 2b2
= a2 + b2 – 2b2 + 6ab
= a2 – b2 + 6ab
(15) (4m2 + 4n2 + 4p2) – (m2 + 3n2 – 5p2)
= 4m2 + 4n2 + 4p2 – m2 – 3n2 + 5p2
= 3m2 + n2 + 9p2
(16) 4x3 – 3x2y – 7xy2 + 2y3 – (3x3 – 2x2y + xy2 – y3)
= 4x3 – 3x2y – 7xy2 + 2y3 – 3x3 + 2x2y – xy2 + y3
= 4x3 – 3x3 – 3x2y + 2x2y – 7xy2 – xy2 + 2y3 + y3
= x3 – x2y – 8xy2 + 3y3
(17) (5a2 – 9a + 3 + 2a – a2 – 1) – (3a2 – 2a + 5 + a2 – 5a – 7)
= 5a2 – 9a + 3 + 2a – a2 – 1 – 3a2 + 2a – 5 – a2 + 5a + 7
= 5a2 – a2 – 3a2 – a2 – 9a + 2a + 2a + 5a + 3 – 1 – 5 + 7
= 5a2 – 5a2 – 9a + 9a + 10 – 6
= 4
(18) Perimeter = 2 × (8x2 + 4x + other side)
⇒ 2 × (8x2 + 4x + other side) = 28x3 + 16x2 + 8x + 4
⇒ 16x2 + 8x + (2 × other side) = 28x3 + 16x2 + 8x + 4
⇒ 2 × other side = 28x3 + 16x2 + 8x + 4 – 16x2 – 8x
⇒ 2 × other side = 28x3 + 4
⇒ 2 × other side = 2 (14x3 + 2)
⇒ other side = 14x3 + 2
(19) Perimeter of a triangle = Sum of its three sides
⇒ (3a2 + 5a + 1 + a2 + 10a – 6 + other side) = 14a2 + 20a + 13
⇒ other side = 14a2 + 20a + 13 – 3a2 – 5a – 1 – a2 – 10a + 6
⇒ other side = 14a2 – 3a2 – a2 + 20a – 5a – 10a + 13 – 1 + 6
⇒ other side = 14a2 – 4a2 + 20a – 15a + 19 – 1
⇒ other side = 10a2 + 5a + 18
(20) (i) x + y + z
= 4a2 + b2 – 6ab + 3b2 – 2a2 + 8ab + 6a2 + 8b2 – 6ab
= 4a2 – 2a2 + 6a2 + b2 + 3b2 + 8b2 – 6ab + 8ab – 6ab
= 10a2 – 2a2 + 12b2 + 8ab – 12ab
= 8a2 + 12b2 – 4ab
(ii) x – y – z
= 4a2 + b2 – 6ab – (3b2 – 2a2 + 8ab) – (6a2 + 8b2 – 6ab)
= 4a2 + b2 – 6ab – 3b2 + 2a2 – 8ab – 6a2 – 8b2 + 6ab
= 4a2 + 2a2 – 6a2 + b2 – 3b2 – 8b2 – 6ab – 8ab + 6ab
= 6a2 – 6a2 + b2 – 11b2 – 8ab
= – 10b2 – 8ab
(21) (i) 2m – n
= 2(9x2 – 4xy + 5y2) – (- 3x2 + 2xy – y2)
= 18x2 – 8xy + 10y2 + 3x2 – 2xy + y2
= 21x2 – 10xy + 11y2
(ii) m + 2n
= 9x2 – 4xy + 5y2 + 2(- 3x2 + 2xy – y2)
= 9x2 – 4xy + 5y2 – 6x2 + 4xy – 2y2
= 3x2 + 3y2
(iii) m – 3n
= 9x2 – 4xy + 5y2 – 3(- 3x2 + 2xy – y2)
= 9x2 – 4xy + 5y2 + 9x2 – 6xy + 3y2
= 18x2 – 10xy + 8y2
(22) Simplify:
(i) 3x + 5(2x + 6) – 7x
= 3x + 10x + 30 – 7x
= 13x – 7x + 30
= 6x + 30
(ii) 3(4y – 10) + 2(y – 1)
= 12y – 30 + 2y – 2
= 14y – 32
(iii) – (7 + 6x) – 7(x + 2)
= – 7 – 6x – 7x – 14
= – 21 – 13x
(iv) x – (x – y) – y – (y – x)
= x – x + y – y – y + x
= x – y
(v) 4x + 7y – (5y – 8) – 2x
= 4x + 7y – 5y + 8 – 2x
= 2x + 2y + 8
(vi) – 2m + 5 + 4(m – 3)
= – 2m + 5 + 4m – 12
= 2m – 7
(vii) 2x – y + 5 – (x – y)
= 2x – y + 5 – x + y
= x + 5
(viii) 2(x – y) – (x – 8)
= 2x – 2y – x + 8
= x – 2y + 8
(ix) 4(3x – 8) – 3(5x + 3) – 2(6x – 8)
= 12x – 32 – 15x – 9 – 12x + 16
= – 15x – 32 + 16 – 9
= – 15x – 16 – 9
= – 15x – 25
(x) 5(x – 4) – 3(x – 4) + 7(x – 4)
= 5x – 20 – 3x + 12 + 7x – 28
= 5x + 7x – 3x – 20 – 28 + 12
= 12x – 3x – 48 + 12
= 9x – 36