1. А) (a+3)(a-7)-2a(3a+5) = а^2 - 7а + 3а - 21 - 6а^2 - 10а = -5а^2 -14а - 21
Б) 4b(b-2)+(b-4)² = 4b^2 - 8b + b^2 - 8b + 16 = 5b^2 - 16b + 16
В) 3(y+2)²-91 = 3 (y^2 + 4y + 4) - 91 = 3y^2 + 12 y + 12 - 91 = 3y^2 + 12 y - 79
2. a) c³-16c = c (c^2 - 16) = c (c-4)(c+4)
b) 3a²-6a+2a² = 5a^2 - 6a = a (5a-6)
3. (3x-x²)²-x²(x+2(x-2)+2x(7+3x³) = 9x^2 - 6x^3 + x^4 - x^2 (x^2 - 4 + 14x + 6x^4) = 9x^2 - 6x^3 + x^4 - x^4 + 4x^2 - 14x^3 - 6x^6 = 13x^2 - 20x^3 - 6x^6
4. a) 16a⁴ - 1 = (4a^2 - 1) (4a^2 + 1) = (2a - 1) (2a + 1) (4a^2 + 1)
b) a-a²+b+b² = (a + b) - (a^2 - b^2) = (a + b) - (a + b) (a - b) = (a + b) (1 - a + b)
1.
А) -8*(x-0,5)*(x-3)
-8*x^2+28*x-12
D=784-384=400
x1=0,5
x2=3
Б) -3*(x-8)*(x+0,5)
-3*x^2+22.5*x+12
D=506,25+144=650,25
x1=-0,5
x2=8
В) -3*(x+8)*(x-0,5)
-3*x^2-22.5*x+12
D=506,25+144=650,25
x1=0,5
x2=-8
Г) - 8*(x+3)*(x+0,5)
-8*x^2-28*x-12
D=784-384=400
x1=-0,5
x2=-3
2.
А) -2*(x-12)*(x+31)
-2*x^2-38*x+744
D=7396
x1=-31
x2=12
Б) 12*(x-2)*(x-31)
12*x^2-396*x+744
D=121104
x1=31
x2=2
В) -2*(x+12)*(x-31)
-2*x^2+38*x+744
D=7396
x1=31
x2=-12
Г ) (x-2)*(x-12)*(x-31)
x^3-45*x^2+458*x-744
3.
3x^2+14x-5=0
D=256
x1=1/3
x2=-5
(3x-1)*(x+5)=3x^2+14x-5
А) (3х-1) (х+5)
4.
(9х^2-6х+1)/(6х^2+х-1)=(3x-1)^2/(2x+1)(3x-1)=(3x-1)/(2x+1)
A) (3x-1)/(2x+1)
Объяснение: