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magamed
@magamed
June 2021
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Bonjour,
Je doit factoriser ces calcules pour demain, j'ai (assez) compris la factorisation mais je suis vraiment bloqué :
a) (2x+3)² - 49
b)(2x+x)² - (4x+5)²
c) 25-(3x-1)
d)(4x+1)²-(7-2x)²
merci
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slyz007
Verified answer
A) (2x+3)²-49=(2x+3)²-7² de la forme a²-b²
(2x+3)²-7²=(2x+3+7)(2x+3-7)=(2x+10)(2x-4)=4(x+5)(x-2)
b) (2x+x)²-(4x+5)²=(3x)²-(4x+5)²
(2x+x)²-(4x+5)²=(3x+4x+5)(3x-4x-5)
(2x+x)²-(4x+5)²=(7x+5)(-x-5)=-(7x+5)(x+5)
c) 25-(3x-1)²=5²-(3x-1)²
25-(3x-1)²=(5+3x-1)(5-3x+1)
25-(3x-1)²=(3x+4)(6-3x)=3(3x+4)(2-x)
d) (4x+1)²-(7-2x)²=(4x+1+7-2x)(4x+1-7+2x)
(4x+1)²-(7-2x)²=(2x+8)(6x-6)=12(x+4)(x-1)
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Verified answer
A) (2x+3)²-49=(2x+3)²-7² de la forme a²-b²(2x+3)²-7²=(2x+3+7)(2x+3-7)=(2x+10)(2x-4)=4(x+5)(x-2)
b) (2x+x)²-(4x+5)²=(3x)²-(4x+5)²
(2x+x)²-(4x+5)²=(3x+4x+5)(3x-4x-5)
(2x+x)²-(4x+5)²=(7x+5)(-x-5)=-(7x+5)(x+5)
c) 25-(3x-1)²=5²-(3x-1)²
25-(3x-1)²=(5+3x-1)(5-3x+1)
25-(3x-1)²=(3x+4)(6-3x)=3(3x+4)(2-x)
d) (4x+1)²-(7-2x)²=(4x+1+7-2x)(4x+1-7+2x)
(4x+1)²-(7-2x)²=(2x+8)(6x-6)=12(x+4)(x-1)