h.hofstede (h.hofstede@hogeland.nl)

       
1. a. (x + 4)(x + 5) = x2 + 4x + 5x + 20 = x2 + 9x + 20  
  b. (x + 7)(x - 3) = x2 - 3x + 7x - 21 = x2 + 4x - 21  
  c (a - 5)(a - 6) = a2 - 6a - 5a + 30 = a2 - 11a + 30  
  d. (p + 3)(2p + 2) = 2p2 + 2p + 6p + 6 = 2p2 + 8p + 6  
  e. (b - 4)(5 + 3b) = 5b + 3b2 - 20 - 12b = 3b2 - 7b - 20  
  f. (2k - 2)(k - 4) = 2k2 - 8k - 2k + 8 = 2k2 - 10k + 8  
  g. (3 - 2h)(3h + 1) = 9h + 3 - 6h2 - 2h = -6h2 + 7h + 3  
  h. (2 - 3p)(-3p - 2) = -6p - 4 + 9p2 + 6p  = 9p2 - 4  
  i. (x - 6)(x + 6) = x2 + 6x - 6x - 36 = x2 - 36  
  j. (x + y)(2x + 3y) = 2x2 + 3xy + 2xy + 3y2 = 2x2 + 5xy + 3y2  
  k. (2a - 4)(7 - a) = 14a - 2a2 - 28 + 4a = -2a2 + 18a - 28  
  l. (3x - 1)(x + 2) - 5x = 3x2 + 6x - x - 2 - 5x =  3x2 - 2  
  m. (2x + 4)(2x - 3) - 4x2  = 4x2 - 6x + 8x - 12 - 4x2 = 2x - 12  
  n. q2 + (-1 - q)(2q + 2) + 4q  = q2 - 2q - 2 - 2q2 - 2q + 4q = -q2 - 2  
       
2. a. (x + 2)2 = (x + 2)(x + 2) = x2 + 2x + 2x + 4 = x2 + 4x + 4  
  b. (x - 5)2 = (x - 5)(x - 5) = x2 - 5x - 5x + 25 = x2 - 10x + 25  
  c. (6 + 3x)2 = (6 + 3x)(6 + 3x) = 36 + 18x + 18x + 9x2 = 9x2 + 36x + 36  
  d. (2a + b)2 = (2a + b)(2a + b) = 4a2 + 2ab + 2ab + b2 = 4a2 + 4ab + b2  
  e. 2(x + 1)2 = 2(x + 1)(x + 1) = 2(x2 + x + x + 1) = 2(x2 + 2x + 1) = 2x2 + 4x + 2
  f. 2 + 4(x - 2)2 = 2 + 4(x - 2)(x - 2) = 2 + 4(x2 - 2x - 2x + 4) = 2 + 4(x2 - 4x + 4) = 2 + 4x2 - 16x + 16
= 4x2 - 16x + 18
  g. 3x(2 + x)2 = 3x(2 + x)(2 + x) = 3x(4 + 2x + 2x + x2) = 3x(x2 + 4x + 4) = 3x3 + 12x2 + 12
  h. x2 - (x - 4)2 = x2 - (x - 4)(x - 4) = x2 - (x2 - 4x - 4x + 16) = x2 - ( x2 - 8x + 16) = x2 - x2 + 8x - 16
= 8x - 16
  i. 5x + (1 + 2x)2 + x2 = 5x + (1 + 2x)(1 + 2x) + x2  = 5x + 1 + 2x + 2x + 4x2 + x2 = 5x2 + 9x + 1
  j. p2(2p - 3)2  = p2(2p - 3)(2p - 3) = p2(4p2 - 6p - 6p + 9) = p2 (4p2 - 12p + 9) =  4p4 - 12p3 + 9p2
       
3. a. (x + 1)(x - 2)(x + 3)
= (x + 1)(x2 + 3x - 2x - 6)
= (x + 1)(x2 + x - 6)
= x3 + x2 - 6x + x2 + x - 6
= x3 + 2x2 - 5x - 6
 
       
  b. (a + 2)(b + 3)(a - 2)
= (a + 2)(ab - 2b + 3a - 6)
= a2b - 2ab + 3a2 - 6a + 2ab - 4b + 6a - 12
= a2b + 3a2 - 4b - 12
 
       
  c. (x + 4)3
= (x + 4)(x + 4)(x + 4)
= (x + 4)(x2 + 4x + 4x + 16)
= (x + 4)(x2 + 8x + 16)
= x3 + 8x2 + 16x + 4x2 + 32x + 64
= x3 + 12x2 + 48x + 84
 
       
  d. (2p - 3)3
= (2p - 3)(2p - 3)(2p - 3)
= (2p - 3)(4p2 - 6p - 6p + 9)
= (2p - 3)(4p2 - 12p + 9)
= 8p3 - 24p2 + 18p - 12p2 + 36p - 27
= 8p3 - 36p2 + 54p - 27   
 
       
4. Stel dat er Y staat, dan geldt:

Y(x + 1) + 1  =  (Y - 1)2
Yx + Y + 1 = Y2 - 2Y + 1
Yx + Y = Y2 - 2Y
Y(x + 1) = Y(Y - 2)
x + 1 = Y - 2
Y = x + 3
       

h.hofstede (h.hofstede@hogeland.nl)