1. a) 3x² -12x =3x(x -4)
b) ab -2a +b² -2b =a(b -2) +b(b -2) =(b -2)(a +b)
в) 4x² -9 =(2x -3)(2x +3)
г) x^3 -8x² +16x =x(x² -8x +16) =x(x -4)² =x(x -4)(x -4)
2. a) (15 -5y) /(9 -y²) =5(3 -y) /(3 -y)(3 +y) =5 /(3 +y)
b) (m² -4mn +4n²) /(m² -4n²) =(m -2n)² /(m -2n)(m +2n) =(m -2n) /(m +2n)
3. x^3 -64x =0
x(x² -64) =0
x =0
x² -64 =0, (x -8)(x +8) =0
x -8 =0, x =8
x +8 =0, x= -8
ответ: x= -8, x =0, x =8
4. x² -12x +32 =(x -8)(x -4)
(x -8)(x -4) =x² -4x -8x +32 =x² -12x +32
те (x -8)(x -4) =(x -8)(x -4),
что и требовалось доказать
5. (87*43) +(87^3 -43^3)/44 =(87*43) +(87 -43)(87² +87*43 +43²)/44 =(87*43) +44*(87² +87*43 +43²) /44 =87*43 +87² +87*43 +43² =87² +2*87*43 +43² =(87 +43)² =130² =16900
(87*43) + (87*43) =2*87*43