Question

Помогите,проверить надо!
Разложите на множители:
5x²-45
-2ay²+2a³
ax²+4ax+4a
-3x²+12x-12
ax²-2axy+ay²
-2x²-8x-8
Представьте в виде произведения:
1/2a²-ab+1/2b²
x²(x-3)-2x(x-3)+(x-3)

Answer 1

5x² - 45 = 5(x² - 9) = 5(x² - 3²)=5(x-3)(x+3)
-2ay² +2a³  = 2a(-y² + a²) = 2a(a² -y²) = 2a(a-y)(a+y)
ax²+4ax +4a  = a(x² + 4x + 4)= a(x² + 2*x*2 + 2²) = a(x+2)²= a(x+2)(x+2)
-3x²+12x-12 = -3(x² -4x + 4) = -3(x² -2*x*2 + 2²) = - 3(x-2)² = -3(x-2)(x-2)
ax²-2axy+ay² =a(x² -2xy+y²) =a(x-y)² =a(x-y)(x-y)
-2x²-8x - 8 = - 2(x² +4x + 4) = - 2(x² +2*x*2 + 2²) = -2(x+2)² =-2(x+2)(x+2)

¹/₂a² - ab  +¹/₂b²  = ¹/₂ * (a² - 2ab + b²) = 0.5(a-b)² = 0.5(a-b)(a-b)
x²(x-3) -2x(x-3) + (x-3) = (x-3) *(x² -2x + 1) = (x-3)(x-1)²= (x-3)(x-1)(x-1)