factoriser
[tex] 64x^{3}+125-( x^{2} + \frac{5}{4} x)[/tex]
[tex] \sqrt{2} x^{3} - \frac{3 \sqrt{3} }{2} [/tex]

Répondre :

64x³+125-(x²+5/4x)
=(4x)³+5³-(x²+5/4x)
=(4x+5)((4x)²-5(4x)+5²)-(x²+5/4x)
=4(x+5/4)(16x²-20x+25)-x(x+5/4)
=(x+5/4)(64x²-80x+100-x)
=(x+5/4)(64x²-81x+100)

√2x³-(3√3)
=√2(x³-(√3/√2)³)
=√2(x-√3/√2)(x²+√3/√2x+3/2)

À retenir :
a³-b³=(a-b)(a²+ab+b²)
a³+b³=(a+b)(a²-ab+b²)