Question

разложите многочлен на множители: (5a+4)^3-a^3
8x^3-(5x-3)^3

Answer 1

Formula: x³-y³=(x-y)(x²+xy+y²)

(5a+4)³-a³=(5a+4-a)(25a²+60a+16+5a²+4a+a²)=
=(4a+4)(31a²+64a+16)=4(a+1)(31a²+64a+16)

8x³-(5x-3)³=(2x)³-(5x-3)³=(2x-5x+3)(4x²+10x²-6x+25x²+30x+9)=
=(-3x+3)(39x²+24x+9)=-3(x-1)(39x²+24x+9)