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laura81
@laura81
June 2021
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36-12x+x^2+(3-4x)(6-x)
Factoriser l'expression ci-dessus.
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Thomas1106
36-12x+x² = (6)²-2*6*x+(x)²
Cette expression est de la forme a²-2ab+b² avec a = 6 et b = x
Rappel :
a²-2ab+b² = (a-b)²
36-12x+x² = (6-x)²
36-12x+x^2+(3-4x)(6-x)
= (6-x)²+(3-4x)(6-x)
= (6-x)(
6-x
)+(3-4x)(
6-x
)
Tu remarques l'existence d'un facteur commun :
6-x
(6-x)(
6-x
)+(3-4x)(
6-x
) = (6-x)(6-x+3-4x) =
(6-x)(-5x+9)
2 votes
Thanks 3
charlotte49
Bonjour ,
Factoriser:
=36-12x+x²+(3-4x)(6-x) [
36 - 12x +x² = ( 6 - x)² ]
= (6 -x)² +(3 - 4x) ( 6 - x)
=( 6 -x) [ (6 -x) +(3 - 4x)]
= ( 6 - x) ( 6 - x +3 -4x)
= (6 -x) ( 9 -5x)
Rappel :
(a - b) = a² - 2*a*b +b²
(a + b) = a² + 2*a*b +b²
a² - b² = (a - b) ( a + b)
0 votes
Thanks 1
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Lista de comentários
Cette expression est de la forme a²-2ab+b² avec a = 6 et b = x
Rappel : a²-2ab+b² = (a-b)²
36-12x+x² = (6-x)²
36-12x+x^2+(3-4x)(6-x)
= (6-x)²+(3-4x)(6-x)
= (6-x)(6-x)+(3-4x)(6-x)
Tu remarques l'existence d'un facteur commun : 6-x
(6-x)(6-x)+(3-4x)(6-x) = (6-x)(6-x+3-4x) = (6-x)(-5x+9)
Factoriser:
=36-12x+x²+(3-4x)(6-x) [ 36 - 12x +x² = ( 6 - x)² ]
= (6 -x)² +(3 - 4x) ( 6 - x)
=( 6 -x) [ (6 -x) +(3 - 4x)]
= ( 6 - x) ( 6 - x +3 -4x)
= (6 -x) ( 9 -5x)
Rappel :
(a - b) = a² - 2*a*b +b²
(a + b) = a² + 2*a*b +b²
a² - b² = (a - b) ( a + b)