1)(a+b)³-(a-b)³
a³+3a²b+3ab²+b³-a³-3a²b+3ab²-b³
6ab²
2)(2x+y)³+(x-2y)³
(2x)³+3*(2x)²*y+3*2x*y²+y³+x³-3*x²*2y+3*x*(2y)²-(2y)³
8x³+12x²y+6xy²+y³+x³-6x²y+12xy²-8y³
9x³+6x²y+18xy²-7y³
3)(2mn-1)³+1
(2mn)³-3*(2mn)²*1+3*2mn*1²-1³+1
8m³n³-12m²n²+6mn-1+1
8m³n³-12m²n²+6mn
4)(3a-2b)³+8b³
(3a)³-3*(3a)²*2b+3*3a*(2b)²-(2b)³+8b³
27a³-54a²b+36ab²-8b³+8b³
27a³-54a²b+36ab²
Через дискриминант
x2-6x+8
D=36-(4*1*8)=4
x1=6+2/2=4
x2=6-2/2=2
Решение
2x² - y² = 34
xy = 20
y = 20/x
2x² - (20/x)² = 34
2x² - 400/x² - 34 = 0
x⁴ - 17x² - 200 = 0
x² = t, t ≥ 0
t² - 17t - 200 = 0
D = 289 + 4*1*200 = 1089
t₁ = (17 - 33)/2
t₁ = - 8 не удовлетворяет условию t ≥ 0
t₂ = (17 + 33)/2
t₂ = 25
x² = 25
x₁ = - 5
x₂ = 5
x₁= - 5
y₁ = 20/(-5)
y₁ = - 4
x₂ = 5
y₂ = 20/5
y₂ = 4
Ответ: (- 5; - 4) (5; 4)