Question

Упростить выражение:
1)y(y-5)(y+5)-(y+2)(y^2-2y+4)
разложите на множители:
a^2-36b^2+a-6b
4-m^2+14mn-49n^2
решите уравнение:
2x^3-32x=0
81x^3+18x^2+x=0
x^3+6x^2-x-6=0

Answer 1

 y(y - 5)(y + 5) - (y + 2)(y² - 2y + 4)= y(y² - 25) - (y³ + 2³) = y³ - 25y - y³ - 8 =
= 8-25y

a² - 36 b² + a - 6b = (a² - 36b²) + (a - 6b) = (a - 6b)(a + 6b) + (a - 6b) =
= (a - 6b)(a + 6b + 1)

4 - m² + 14mn - 49n² = 4 - (m² - 14mn + 49n²) = 2² - (m - 7n)² =
= (2 - m + 7n)(2 + m - 7n)

2x³ - 32x = 0
2x(x² - 16) = 0
x(x - 4)(x + 4) = 0
или  x₁ = 0       или  x - 4 = 0             или    x + 4 = 0
                                x₂ = 4                           x₃ = - 4

81x³ + 18x² + x = 0
x(81x² + 18x + 1) = 0
x(9x + 1)² = 0
или  x₁ = 0            или   9x + 1 = 0
                                       9x = - 1
                                       x₂ = - 1/9

x³ + 6x² - x - 6 = 0
(x³ - x) + (6x² - 6) = 0
x(x² - 1) + 6(x² - 1) = 0
(x² - 1)(x + 6) = 0
(x - 1)(x + 1)(x + 6) = 0
или x - 1 = 0              или  x + 1 = 0            или  x + 6 = 0
       x₁ = 1                          x₂ = - 1                       x₃ = - 6