Selina Concise Class 6 Math Chapter 17 Fundamental Operations Exercise 17C Solution
EXERCISE 17C
(i) 6 × 3 = 18 and 6x × 3x = 18x2
(ii) 6 × 3 = 18 and 6x2 × 3x3 = (6 × 3) (x2+3) = 18x5
(iii) 5 × 4 = 20 and 5x × 4y = 20xy
(iv) 4 × 7 = 28 and 4ax × 7x = 28ax2
(v) 6 × 2 = 12 and 6xy × 2xy = (6 × 2) x1+1 y1+1 = 12x2y2
(vi) 12 × 4 = 48 and 12ax2 × 4ax = (12 × 4) a1+1 x2+1 = 48a2x3
(vii) 1 × 8 = 8 and a2xy2 × 8a3x2y = 8a2+3 x1+2 y2+1 = 8a5x3y3
(viii) 15 × 3 = 45 and 15x × 3x5y2 = (15 × 3) x1+5 y2 = 45x6y2
(2) Fill in the blanks:
(i) 4x × 6x × 2 = (4 × 6 × 2) x1+1 = 48x2
(ii) 3ab × 6ax = (3 × 6) a1+1 bx = 18a2bx
(iii) x × 2x2 × 3x3 = (2 × 3) x1+2+3 = 6x6
(iv) 5 × 5a3 = 25a3
(v) 6 × 6x2 × 6x2y2 = (6 × 6 × 6) x2+2 y2 = 216 x4y2
(vi) – 8x × (- 3x) = 24x1+1 = 24x2
(vii) – 5 × – 3x × 5x2 = (5 × 3 × 5) x1+2 = 75x3
(viii) 8 × (- 4xy2) × 3x3y2 = – (8 × 4 × 3) x1+3 y2+2 = – 96 x4 y4
(ix) – 4x × 5xy × 3z = – (4 × 5 × 3) x1+1 yz = – 60x2yz
(x) 5x × 2x2y × (- 7y3) × 2x3y2
= – (5 × 2 × 7 × 2) x1+2+3 y1+3+2
= – 140 x6 y6
(3) Find the value of:
(i) 3x3 × 5x4 = (3 × 5) x3+4 = 15 x7
(ii) 5a2 × 7a7 = (5 × 7) a2+7 = 35 a9
(iii) 3abc × 6ac3 = (3 × 6) a1+1 b c1+3 = 18 a2bc4
(iv) a2b2 × 5a3b4 = 5a2+3b2+4 = 5a5b6
(v) 2x2y3 × 5x3y4 = (2 × 5) x2+3 y3+4 = 10 x5y7
(vi) abc × bcd = ab1+1c1+1d = ab2c2d
(4) Multiply:
(i) (a + b) × ab
= (a × ab) + (b × ab)
= a1+1b + b1+1a
= a2b + ab2
(ii) (3ab – 4b) × 3ab
= (3ab × 3ab) – (4b × 3ab)
= (3 × 3)a1+1b1+1 – (4 × 3) ab1+1
= 9a2b2 – 12ab2
(iii) (2xy – 5by) × 4bx
= (2xy × 4bx) – (5by × 4bx)
= (2 × 4) x1+1 by – (5 × 4)b1+1xy
= 8x2by – 20b2xy
(iv) (4x + 2y) × 3xy
= (4x × 3xy) + (2y × 3xy)
= 12x1+1y + 6xy1+1
= 12x2y + 6xy2
(v) (x2 – x) × 2x
= (x2 × 2x) – (x × 2x)
= 2x2+1 – 2x1+1
= 2x3 – 2x2
(vi) (1 + 4x) × x
= x + 4x2
(vii) (9xy2 + 3x2y) × 5xy
= (9 × 5) x1+1y2+1 + (3 × 5)x2+1y1+1
= 45x2y3 + 15x3y2
(viii) (6x – 5y) × 3axy
= (6 × 3) x1+1ay – (5 × 3)axy1+1
= 18ax2y – 15axy2
(5) Multiply:
(i) (- x + y – z) × (- 2x)
= 2x1+1 – 2xy + 2xz
= 2x2 – 2xy + 2xz
(ii) (xy –yz) × (x2yz2)
= x1+2y1+1z2 – x2y1+1z1+2
= x3y2z2 – x2y2z3
(iii) (2xyz + 3xy) × (- 2y2z)
= – (2 × 2) xy1+2z1+1 – (3 × 2)ay1+2z
= – 4xy3z2 – 6ay3z
(iv) (- 3xy2 + 4x2y) × (- xy)
= 3x1+1y2+1 – 4x2+1y1+1
= 3x2y3 – 4x3y2
(v) 4xy × (- xy2 – 3x2y2)
= – 4x1+1y1+2 – (4 × 3) x1+2y1+2
= – 4x2y3 – 12x3y3
(6) Multiply:
(i) (3a + 4b – 5c) × 3a
= (3 × 3)a1+1 + (4 × 3)ab – (5 × 3)ac
= 9a2 + 12ab – 15ac
(ii) – 5xy × (- xy2 – 6x2y)
= 5x1+1y1+2 + (5 × 6)x1+2y1+1
= 5x2y3 + 30x3y2
(7) Multiply:
(i) (x + 2) × (x + 10)
= (x × x) + (2 × x) + (x × 10) + (2 × 10)
= x2 + 2x + 10x + 20
= x2 + 12x + 20
(ii) (x + 5) × (x – 3)
= (x × x) + (5 × x) – (3 × x) – (5 × 3)
= x2 + 5x – 3x – 15
= x2 + 2x – 15
(iii) (x – 5) × (x + 3)
= (x × x) – (5 × x) + (3 × x) – (5 × 3)
= x2 – 5x + 3x – 15
= x2 – 2x – 15
(iv) (x – 5) (x – 3.)
= (x × x) – (5 × x) – (3 × x) + (5 × 3)
= x2 – 5x – 3x + 15
= x2 – 8x + 15
(v) (2x + y) × (x +3y)
= (2x × x) + (y × x) + (2x × 3y) + (y × 3y)
= 2x2 + xy + 6xy + 3y2
= 2x2 + 7xy + 3y2
(vi) (3x – 5y) × (x + 6y)
= (3x × x) – (5y × x) + (3x × 6y) – (5y × 6y)
= 3x2 – 5xy + 18xy – 30y2
= 3x2 + 13xy – 30y2
(vii) (x + 9y) × (x – 5y)
= (x × x) + (9y × x) – (x × 5y) – (9y × 5y)
= x2 + 9xy – 5xy – 45y2
= x2 + 4xy – 45y2
(viii) (2x + 5y) × (2x + 5y)
= (2x × 2x) + (5y × 2x) + (2x × 5y) + (5y × 5y)
= 4x2 + 10xy + 10xy + 25y2
= 4x2 + 20xy + 25y2
(8) Multiply:
(i) 3abc × (- 5a2b2c)
= – (3 × 5) a1+2b1+2c1+1
= – 15a3b3c2
(ii) (x – y + z) × (- 2x)
= – (x × 2x) + (y × 2x) – (z × 2x)
= – 2x2 + 2xy – 2xz
(iii) (2x – 3y – 5z) × (- 2y)
= – (2x × 2y) + (3y × 2y) + (5z × 2y)
= – 4xy + 6y2 + 10yz
(iv) (– 8xyz + 10x2yz3) × xyz
= – 8x1+1y1+1z1+1 + 10x2+1y1+1z3+1
= – 8x2y2z2 + 10x3y2z4
(v) xyz × (- 13xy2z + 15x2yz – 6xyz2)
= – 13x1+1y1+2z1+1 + 15x1+2y1+1z1+1 – 6x1+1y1+1z1+2
= – 13x2y3z2 + 15x3y2z2 – 6x2y2z3
(vi) 4abc – 5a2bc – 6ab2c × (- 2abc2)
= – (4 × 2)a1+1b1+1c1+2 + (5 × 2)a2+1b1+1c1+2 + (6 × 2)a1+1b2+1c1+2
= – 8a2b2c3 + 10a3b2c3 + 12a2b3c3
(9) Find the product of:
(i) (xy – ab) × (xy + ab)
= (xy × xy) – (ab × xy) + (xy × ab) – (ab × ab)
= x2y2 – abxy + abxy – a2b2
= x2y2 – a2b2
(ii) (2abc – 3xy) × (2abc + 3xy)
= (2abc × 2abc) – (3xy × 2abc) + (2abc × 3xy) – (3xy × 3xy)
= 4a2b2c2 – 6abcxy + 6abcxy – 9x2y2
= 4a2b2c2 – 9x2y2
(iii) (a + b – c) × (2a – 3b)
= (a × 2a) + (b × 2a) – (c × 2a) – (a × 3b) – (b × 3b) + (c × 3b)
= 2a2 + 2ab – 2ac – 3ab – 3b2 + 3bc
= 2a2 – ab – 2ac – 3b2 + 3bc
(iv) (5x – 6y – 7z) × (2x + 3y)
= (5x × 2x) – (6y × 2x) – (7z × 2x) + (5x × 3y) – (6y × 3y) – (7z × 3y)
= 10x2 – 12xy – 14xz + 15xy – 18y2 – 21yz
= 10x2 + 3xy – 14xz – 18y2 – 21yz
(v) (5x – 6y – 7z) × (2x + 3y + z)
= (5x × 2x) – (6y × 2x) – (7z × 2x) + (5x × 3y) – (6y × 3y) – (7z × 3y) + (5x × z) – (6y × z) – (7z × z)
= 10x2 – 12xy – 14xz + 15xy – 18y2 – 21yz + 5xz – 6yz – 7z2
= 10x2 + 3xy – 9xz – 18y2 – 27yz – 7z2
(vi) (2a + 3b – 4c) × (a – b – c)
= (2a × a) + (3b × a) – (4c × a) – (2a × b) – (3b × b) + (4c × b) – (2a × c) – (3b × c) + (4c × c)
= 2a2 + 3ab – 4ac – 2ab – 3b2 + 4bc – 2ac – 3bc + 4c2
= 2a2 + ab – 6ac – 3b2 + bc + 4c2