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Sousou299
@Sousou299
January 2021
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Pouvez vous m’aidez
Factorises les expressions
2(2x+3)(4x-5)+(2x+3)2+(4x-5)2
Les deux derniers 2 sont des carré après les parenthèses
Merci d’avance
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mathmate
Première étape: développer l'expression
2(2x+3)(4x-5)+(2x+3)2+(4x-5)2
=
2(2x+3)(4x-5)+(2x+3)^2+(4x-5)^2
=2(8x^2+2x-15)+(4x^2+12x+9)+(16x^2-40x+25)
=36x^2-24x+4
ensuite, factoriser
=4(9x^2-6x+1) [ carré parfait]
=4(3x-1)^2
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2(2x+3)(4x-5)+(2x+3)2+(4x-5)2
=2(2x+3)(4x-5)+(2x+3)^2+(4x-5)^2
=2(8x^2+2x-15)+(4x^2+12x+9)+(16x^2-40x+25)
=36x^2-24x+4
ensuite, factoriser
=4(9x^2-6x+1) [ carré parfait]
=4(3x-1)^2