factoriser : D(t)=(5t-1)(3t-2)-(5t-1)² A(t)=(3t+1)²-(4t-1)² B(t)=9(t+1)²-4(2t+3)² C(t)=t²+2t+1+(t+1)(3t-5)

A(t)=(3t+1)²-(4t-1)²                            [ a² - b² = ( a - b ) ( a + b )  ]
     =  [ (3t+1) - (4t-1) ] [ (3t+1) + (4t-1) ]
     =  [ 3t +1 - 4t +1 ] [ 3t + 1 + 4t -1 ]
     =  [ -t +2  ] [ 7t ]
     =  7t ( 2 - t )

B(t)=9(t+1)²-4(2t+3)²
      = 3² (t+1)²- 2² (2t+3)²
      = [3 (t+1) ]²- [2 (2t+3) ]²                               [ a² - b² = ( a - b ) ( a + b )  ]
      = [ 3 (t+1) - 2 (2t+3)]  [ 3 (t+1) + 2 (2t+3)]
      = [ 3 t + 3 - 4t - 6 ]  [ 3 t + 3 + 4t + 6 ]
      = ( -t - 3 )  ( 7 t + 9 )


C(t)=t²+2t+1+(t+1)(3t-5)                                     (  a² + 2ab + b² = ( a + b )²  )
     = (t + 1)² + (t+1) (3t-5)                            (t + 1) est un facteur en commun 
      = (t + 1) [  (t +1) + (3t - 5) ]
      = (t + 1) [ t + 1 + 3t - 5 ]
      = (t + 1) ( 4t - 4 )
      = (t + 1) 4 ( t - 1 )
      = 4 (t + 1) ( t - 1 )

D(t) = ( 5t - 1) ( 3t - 2) - ( 5t - 1)²                ( 5t - 1) est un facteur en commun
      = ( 5t - 1) [ ( 3t - 2) - ( 5t - 1) ]
      = ( 5t - 1) [ 3t - 2 - 5t + 1 ]
      = ( 5 t - 1) ( -2 t - 1 )

Bonjour

A(t) = (3t+1)²-(4t-1)²
A(t) = [(3t+1) + (4t-1)][(3t+1) - (4t-1)]
A(t) = (3t+1+4t-1)(3t+1-4t+1)
A(t) = (7t)(-t+2)

B(t) = 9(t+1)²-4(2t+3)²
B(t) = [3(t+1) + 2(2t+3)][3(t+1) - 2(2t+3)]
B(t) = (3t+3 + 4t+6)(3t+3 - 4t-6)
B(t) = (7t+9)(-t-3)

C(t) = t ²+ 2t + 1 + (t+1)(3t-5)
C(t) = (t+1)² + (t+1)(3t-5)
C(t) = (t+1)(t+1) +(t+1)(3t-5)
C(t) = (t+1)[(t+1)+(3t-5)]
C(t) = (t+1)(t+1+3t-5)
C(t) = (t+1)(4t-4)

D(t) = (5t-1)(3t-2)-(5t-1)²
D(t) = (5t-1)(3t-2)-(5t-1)(5t-1)
D(t) = (5t-1)[(3t-2)-(5t-1)]
D(t) = (5t-1)(3t-2-5t+1)
D(t) = (5t-1)(-2t-1)