2х²+4ху + 2у² = 2(х²+2ху + у²)=2(x+y)²
3а² - 6а + 3 =3(а² - 2а + 1)= 3(a+1)²
2ху² + 4 ху + 2х =2x(y²+2y+1)=2x(y+1)²
6х² -12ху + 6у² =6(х² -2ху + у²)=6(x-y)²
5m²+10m + 5 =5(m²+2m+1)=5(m+1)²
3а - 6аb + 3аb² = 3a(1-2b+b²)=3a(1-b)²
(√2 - 2√7)^2 = 2 - 2*√2*2√7 + 4*7 = 2 - 4√14 + 28 = 30 - 4√14
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