FACTORISATION (1)

 

Mise en évidence

 

Exemples :

Dividende

=

diviseur

.

quotient

=

4a³b²

.

a - 4ac + ax

=

a

.

(1 - 4c + x)

5(a+b)-a(a+b)

=

(a+b)

.

(5-a)

7(x-y) + a( y-x )

=

( x-y )

.

(7 - a)
N.B: le diviseur est le PGCD des termes du dividende . Attention au changement de signe !

Factorise :

7a-7ab+7 =

ab+a-7ac =

3xy+6xz-3x =

ax+4axy+axc =

8aby-8by+16bxy=

-4a7b³+6a5b5-2a6b³ =

b(x-y) + 9(x-y) =

(a+b)+2x(a+b)-9y(a+b) =

3(a-b)(x-y)-(4a-b)(x-y) =

3(a+b)-(a+b)² =

(a-b)-3(a-b)(a-4)+2(a-b)² =

a(x-y)-2b(y-x) =

y(x-a)-(a-x) =

3a(b-y)-(y-b)(2a+x) =

(x-y)(a-b)-(2a-b)(y-x) =

3(x-y)(a+b)+(2y-2x)(b+a) =

2ab4-2b²+6b³c =

x³y-x²y³+2x²yz+3x²y =

 

Groupements

Exemples :

  1. ad+bd+ay+by = (ad+bd) + (ay+by) = d(a+b) + y(a+b) = (a+b).(d+y)
  2. 2x+ax-2y-ay = (2x-2y) + (ax-ay) = 2(x-y) + a(x-y) = (x-y).(2+a)

ab+bx+ay+xy =

ay-xy-ab+bx =

ab+ay+2b+2y =

3xy+3x²+2ay+2ax =

9ax-ay-9bx+by =

ab-x-a+bx =

12ax-9ay-8x+6y =

4a²-2ab+b²-2ab =

x²y-bxy+abx-ab² =

abx+2ax+bx+2x-aby-by =

 

Différence de carrés

Exemples :

  1. a²-b² = (a+b).(a-b)
  2. 4a²-25b8 = (2a+5b4).(2a-5b4)

a²-x² =

x²-9 =

25-b² =

a²-1 =

9x²-a² =

16a²-9b² =

a²b²-x²y² =

 

Corrigé factorisation (1)