Lezione 6 Esercizi di Matematica

                                                                                                                           AVANTI

• 1) ( 3x2-5x+2)+(2x2-3x+4)-( 4x2-8x+5)
  

=3x2-5x+2x2-3x+4-4x2+8x-5

=5x2-4x2-5x-3x+8x+2+4-5

=x2+1 //

• 2) 3x2-[5ab-(b2-4a2)-(2ab-3b2)-(a2+3ab)]
  

= 3a2-[5ab-b2+4a2-2ab+3b2-a2-3ab]

= 3a2-5ab+b2-4a2+2ab-3b2+a2+3ab

= -2b2 //

• 3) 3a2-(1/3a2b-a4)+[a2-1/2a4 - (1/6a2b+4a2)]
  

= 3a2-1/3a2b+a4+[a2-1/2a4-1/6a2b-a4]

=3a2-1/3a2b+a4+a2-1/2a4-1/6a2b-a4

=-1/2a4+4a2+(-2-1)/6a2b

=-1/2a4+4a2-3/6a2b

=1/2a4+4a2-1/2a2b //

• 4)[(-3x)2 + (-2xy)2 ] + (-4x2y2+5x2) - (-6x)3 : (-9x)
  

=[9x2+4x2y2] -4x2y2+5x2-(-216x3):(-9x)

=9x2+4x2y2-4x2y2+5x2-24x2

=-10x2 //

• 5)[2b5:(-b2)2+13+5] - [4b+(3bc)3:(-b3c2)+8]+3
  

=[2b5:b4+3c+5]-è4b+27b3c3:-b3c2+8]+3

=[2b+3c+5]-[4b-27c+8]+3

=2b+3c+5-4b+27c-8+3

=-2b+30c //

• 6) [(-2ax2)2 - [3/2a3-1/2a2x4+(-3a)a3-(3 x3-1/2a2x4)]-3x3
  

=4a2x4-[3/2a3-1/2a2x4-27a3-3x3+1/2a2x4]-3x

=4a2x4-3/2a3+1/2a2x4+27a3+3x3-1/2a2x4-3x3

=4a2x4+(-3+54):2a3

=4a2x4+51/2a3 //

• 7) (1/3m2)3-m4-[3/4m2n2-(1/2m3)2+[(-2m)4+1/4m2n2-8/27m6)]
  

= 1/27m6-m4-[3/4m2n2-1/4m6+[16m4+1/4m2n2-8/27m6]]

=1/27m6-m4-3/4m2n2+1/4m6-16m4-1/4m2n2+8/27m6

=(1/27+1/4+8/27)m6+(-m4-16m4)+(-3/4-1/4)m2n2

=(4+27+32):108m6-17m4+(-3-1):4m2n2

=(63/108)m6-17m4-4/4m2n2

=7/12m6-17m4-m2n2 //

• 8)-2x2(x2-2xy+y2)-(x3-3x2y+y3)(-2x)
  

=-2x4+4x3y-2x2y2-(-2x4+6x3y-2xy3)

=-2x4+4x3y-2x2y2+2x4-6x3y+2xy3

=-2x3y-2x2y2+2xy3 //

• 9) [3a2+(4a-1)(a+1)](2a+3)
  

=[3a2+4a2+4a-a-1](2a+3)

=[7a2+3a-1](2a+3)

=14a3+21a2+6a2+9a-2a-3

=14a3+27a2+7a-3 //