Question

Разложите многочлен на множители 27-8а^3 8x^3+y^3 27a^3-8b^3 1+64y^3 125x^3-27y^3 1-8b^3

Answer 1

27- 8а³ = 3³-2³a³= (3-2a)(3²-2×3×2a+(2a)²)= (3-2a)(9-12a+4a²)
8х³+у³= 2³х³+у³= (2х+у)(4х²-4ху+у²)
27а³-8b³= 3³a³-2³b³=(3a-2b)(9a²-2×3a×2b+4b²)=(3a-2b)(9a²-12ab+4b²)
1+64y³=1³+4³y³=(1+4y)(1²-2×1×4y+(4y)²)= (1+4y)(1-8y+16y²)
125х³-27у³=5³x³-3³y³=(5x-3y)(25x²-30xy+9y²)
1-8b³= 1³-2³b³=(1-2b)(1-4b+4b²)