Sagot :
1. Factoriser l'expression 64-25x²
a²-b²=(a-b)(a+b)
64-25x²=8²-(5x)²
=(8-5x)(8+5x)
2. en deduire la forme factorisée de :
64-25x² -(8x +3)(8-5x)
=(8-5x)(8+5x)-(8x+3)(8-5x)
=(8-5x)(8+5x-(8x+3))
=(8-5x)(8+5x-8x-3)
=(8-5x)(5-3x)
a²-b²=(a-b)(a+b)
64-25x²=8²-(5x)²
=(8-5x)(8+5x)
2. en deduire la forme factorisée de :
64-25x² -(8x +3)(8-5x)
=(8-5x)(8+5x)-(8x+3)(8-5x)
=(8-5x)(8+5x-(8x+3))
=(8-5x)(8+5x-8x-3)
=(8-5x)(5-3x)
Réponse :
Explications étape par étape
64-25x²-(8-5x)²
= 8²- (5x)² - (8-5x)² on utilise l'identité remarquable a²-b²
= (8-5x) (8+5x) - (8-5x) (8-5x)
= (8-5x) [(8+5x) - (8-5x)]
= (8-5x) (5x+5x)
= 10x (8-5x)
