Multiply : 8ab2 by -4a3b4

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asked May 16 in Class VIII Maths by navnit40 (-2,750 points)

Multiply :

(i) 8ab2 by -4a3b4

(ii) (2/3)ab by  -(1/4)a2b

(iii) -5cd2 by – 5cd2

(iv) 4a and (6a + 7)

(v) -8x and (4 – 2x – x2)

(vi) 2a2 – 5a – 4 and -3a

(vii) x + 4 by x – 5

(viii) 5a – 1 by 7a – 3

(ix) 12a + 5b by 7a – b

(x) x2 + x + 1 by 1 – x

(xi) 2m2 – 3m – 11 and 4m2 – m – 1

(xii) a2, ab and b2

(xiii) abx, -3a2x and 7b2x3

(xiv) -3bx, -5xy and -7b3x2

(xv) (-(3/2x5y3) and (4/9 a2x3y)

(xvi) (- (2/3)a7b2 ) and (–(9/4)ab5)

(xvii) (2a3 – 3a2b) and (-(1/2ab2)

(xviii) (2x + (½)y) and (2x – (1/2)y)

 

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1 Answer

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answered May 16 by aditya23 (-606 points)

(i) 8ab2 × -4a3b4 = (8 × -4) (ab2 × a3b4)

= -32a 1+3, b2+4

= - 32a4b6

(ii) (2/3) ab × (-(1/4)a2b ) = (2/3 × (-1/4) (ab × a2b)

= - (1/6)a1+2 . b 1+ 1

= -(1/6)a3b2

(iii) -5cd2 × (-5cd2 )= (-5 × -5) (cd2 × cd2)

= 25c1+1 d2+2

= 25c2d4

(iv) 4a (6a + 7)

= 4a × 6a + 4a × 7

= 24a2 + 28a

(v) -8x (4 – 2x – x2)

= -8x × 4 – 8x × (-2x) – 8x × (-x2)

= -32x + 16x2 + 8x3

(vi) -3a (2a2 – 5a – 4)

= -3a × 2a2 – 5a × (-3a) – 4 × (-3a)

= -6a3 + 15a2 + 12a

(vii) (x + 4) (x -5) = x (x -5) + 4 (x – 5)

= x2 – 5x + 4x – 20

= x2 – x – 20

(viii) (5a – 1) (7a – 3)

= 5a (7a – 3) – 1(7a – 3)

= 35a2 – 15a – 7a + 3

= 35a2 – 22a + 3

(ix) (12a + 5b) (7a – b) = 12a (7a – b) + 5b (7a – b)

= 84a2 – 12ab + 35ab – 5b2

= 84a2 + 23ab – 5b2

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

= x2 + x + 1 – x3 – x2 – x

= 1- x3

(xi) (2m2 – 3m – 1) (4m2 – m – 1)

= 2m2 (4m2 – m – 1) – 3m(4m2 – m – 1) – 1(4m2 – m – 1)

= 8m4 - 2m3 – 2m2 – 12m3 +3m2 + 3m  - 4m2 + m + 1

= 8m4 – 14m3 – 6m2 + 3m2 + 4m + 1

= 8m4 – 14m3 – 3m2 + 4m + 1

(xii) a2 × ab × b2

= a2+1 . b1+2

= a3b3

(xiii)  abx × (-3a2x) × 7b2x3

= (-3 × 7) (a × a2) (b × b2) (x × x × x3)

= -21a3b3x5

(xiv) -3bx × (-5xy) × (-7b3y2)

= (-3 × -5 × -7) (b × b3) (x × x) (y × y2)

= -105 b4 x2y3

(xv) ( -(3/2)x5y3 )  ((4/9)a2x3y)

= ( -(3/2) × 4/9) (a2)(x5 × x3)(y3 × y)

= (-2/3) a2x8y4

(xvi)  (-(2/3)a7 b2)  (-(9/4)ab5)

= (-(2/3) × (-9/4)) (a7 × a) (b2 × b5)

= 3/2 a8b7

(xvii) (2a3 – 3a2b)   (-(1/2)ab2)

=  -(1/2)ab2 (2a3 – 3a2b)

= 2a3 ×  -(½)ab2 – 3a2b ×  -(½) ab2

= - a4b2 + (3/2)a3b3

(xviii) (2x + (½)y ) (2x – ( ½)y)

= 2x (2x – (½)y) + (½)y (2x – (½)y)

= 4x2 – xy + xy – (¼)y2

= 4x2 – (¼)y2

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