Question

f) (x+1)(x+2)(x+3)
g) (3-x)(x+3) (x la put 2 +9)
h) (a-5)(a-1)(a-2)
i) ( 1pe2 a-b) ( 2 pe 3 a+b ) (a-1 pe 3 b)
j) (x+√3)(x+√2)(x-√3)
k) (√5-2√3) (√5a+2√3 )(5a la put 2 +12)
l) ( x la put 2 +x+1)(x la put 2, +2x +3)
m) (2a-b+3)(3a+2b+1)
n) ( 3 a la put 2- 2 a +4 )(a la put 2 -2a -

Answer 1

f) ( x + 1 ) ( x + 2 ) ( x + 3 ) =
   = ( x² + 2x + x + 2 ) ( x + 3 )
   = x³ + 3x² + 2x² + 6x + x² + 3x + 2x + 6
   = X³ + 6x² + 11x + 6
g) ( 3 - x ) (x + 3 ) ( x² + 9 ) =
   = ( 3x + 9 - x² -3x ) ( x² + 9 )
   = ( 9 - x² ) ( x² + 9 )
   = 9x² + 81 - x⁴ - 9x²
   = 81 - x⁴
h) ( a - 5 ) ( a - 1 ) ( a - 2 )
   = ( a² - a - 5a + 5 ) ( a - 2 )
   = ( a² - 6a + 5 ) ( a - 2 )
   = a³ - 2a² - 6a² + 12a + 5a - 10
   = a³ - 8a² + 17a - 10
i) ( 1/2a - b ) ( 2/3a + b ) ( a - 1/3b ) =
  = ( 1/2 x 2/3a² + 1/2ab - 2/3ab - b² ) ( a - 1/3b )
  = ( 1/3a² + 3/6ab - 4/6ab - b² ) ( a - 1/3b )
 = ( 1/3a² - 1/6ab - b² ) ( a - 1/3b )
 = 1/3a³ - 1/9a²b - 1/6a²b + 1/18ab² - ab² + 1/3b³
 = 1/3a³ - 2/18a²b - 3/18a²b + 1/18ab² - 18/18ab² + 1/3b³
 = 1/3a³ + 5/18a²b - 17/18ab² + 1/3b3
j) ( x + √3 ) ( x + √2 ) ( x - √3 ) =
 = ( x² + √2x + √3x + √6 ) ( x - √3 )
 = x³ - √3x² + √2x² - √6x + √3x² - 3x + √6x - √18
 = x³ + √2x² - 3x - 3√2

Answer 2

f) (x + 1)(x + 2)(x + 3)=(x²+2x+x+ 2)(x+ 3)=x³+3x²+2x²+ 6x + x² + 3x + 2x + 6=
= X³ + 6x²+11x+ 6

g) ( 3-x)(x + 3)( x² + 9)=(3x+ 9-x² -3x)(x² + 9) =(9 - x²)(9+x²)= 81-x⁴

h) (a - 5)(a -1)(a - 2)=( a²-a- 5a + 5)(a - 2)=(a²-6a+5)(a -2)=
=a³-2a²-6a²+12a+5a-10=a³-8a²+17a-10

i) ( 1/2a - b)(2/3a+b)(a-1/3b)=(1/2x2/3a²+ 1/2ab-2/3ab-b²)(a-1/3b )=
 =( 1/3a² +3/6ab-4/6ab-b²)( a-1/3b )=(1/3a²-1/6ab -b²)(a-1/3b )=
 =1/3a³-1/9a²b-1/6a²b+1/18ab²-ab²+1/3b³=
 =1/3a³ -2/18a²b-3/18a²b + 1/18ab² -18/18ab² +1/3b³
 = 1/3a³ + 5/18a²b - 17/18ab² + 1/3b³

j) (x+√3)(x+√2)(x-√3)=(x²+√2x+√3x+ √6)(x-√3 )
 =x³-√3x²+√2x²-√6x+√3x²-3x+√6x-√18=x³+√2x²-3x-3√2

k) (√5-2√3)(√5a+2√3 )(5a² +12)=(5a+2√15-2√15a-12)(5a² +12)=
=25a³+60a+10√15a²+24√15-10a³√15-24√15a-60a²-144=
=25a³-10a³√15-60a²+10√15a²+60a-24√15a+24√15-144

l) (x²+x+1)(x²+2x+3)=x⁴+2x³+3x²+x³+2x²+3x+x²+2x+3=
=x⁴+3x³+6x²+5x+3

m) (2a-b+3)(3a+2b+1) =6a²+4ab+2a-3ab-2b²-b+9a+6b+3=
=6a²+ab+11a-2b²+5b+3

vezi ca aici ti-am pus si fisierele cu exercitiile din cele 4 poze de data trecuta