1. a) (3 -a)(3 +a) =9 -a²
b) (b +2a)(2a -b) = -b² +4a²
в) (x² -1)(1 +x²) =x^4 -1
a) (a -4)(a +4) =a² -16
b) (5x +y)(y -5x) = -25x² +y²
в) (1 -x^3)(x^3 +1) =1 -x^6
2. a) y² -100 =(y -10)(y +10)
b) -0.16x² +y² =(0.4x +y)(y -0.4x)
в) a^4 -25 =(a² -5)(a² +5)
a) 49 -x² =(7 -x)(7 +x)
b) -0.01a² +b² =(0.1a +b)(b -0.1a)
в) 9 -a^4 =(3 -a²)(3 +a²)
3. a) (x -1)(x +1) -x(x -2) =0
x² -1 -x² +2x =0
-1 +2x =0
2x =1
x =1/2
x =0.5
b) x² -4 =0
(x -2)(x +2) =0
x -2 =0, x =2
x +2 =0, x = -2
a) (x +2)(x -2) -x(x -3) =0
x² -4 -x² +3x =0
3x =4
x =4/3
x =1 1/3(одна целая одна третья)
b) x² -1 =0
(x -1)(x +1) =0
x -1 =0, x =1
x +1 =0, x = -1
4. a) y^3 +8 =(y+2)(y²-2y+4)
b) a^3 -1 =(a -1)(a² +a +1)
a) y^3 +1000 =(y +10)(y² -10y +100)
b) b^3 -8 =(b -2)(b² +2b +4)
значок ^ обозначает в степени