Разложить двучлены ** множители; b^3+8 x^3+y^6 p^6+q^6 m^6+n^15 27a^3+b^3 x^3+64y^3...

Question

Разложить двучлены на множители;
b^3+8
x^3+y^6
p^6+q^6
m^6+n^15
27a^3+b^3
x^3+64y^3
c^6+125d^3
8p^6+q^12

Answer 1

Пользуемся формулой: a³ + b³ = (a+b)(a²-ab+b²).
b³+8 = b³ + 2³ = (b+2)(b²-2b+4)
x³+y⁶ = x³ + (y²)³ = (x+y²)(x²-xy²+y⁴)
p⁶+q⁶ = (p²)³ + (q²)³ = (p²+q²)(p⁴-p²q²+q⁴)
m⁶+n¹⁵ = (m²)³ + (n⁵)³ = (m²+n⁵)(m⁴-m²n⁵+n¹⁰)
27a³+b³ = (3a)³ + b³ = (3a+b)(9a²-3ab+b²)
x³+64y³ = x³ + (4y)³ = (x+4y)(x²-4xy+16y²)
c⁶+125d³ = (c²)³ + (5d)³ = (c²+5d)(c⁴-5c²d+25d²)
8p⁶+q¹² = (2p²)³ + (q⁴)³ = (2p²+q⁴)(4p⁴-2p²q⁴+q⁸)