Ответ :
[tex]1.\ 2b^5-16b^2=2b^2(b^3-8)=2b^3(b-2)(b^2+2b+4).[/tex]
2. [tex]x^2-4xy+4y^2+2x-4y=(x-2y)^2+2(x-2y)=(x-2y)(x-2y+2).[/tex]
3. [tex]3a-81a^4=3a(1-27a^3)=3a(1-3a)(1+3a+9a^2).[/tex]
4. [tex]9x^2+6xy+y^2-6x-2y=(3x+y)^2-2(3x+y)=(3x+y)(3x+y-2).[/tex]
5. [tex]28x^3+3x^2+3x+1=27x^3+(x+1)^3=(3x+x+1)(9x^2-3x^2-3x+(x+1)^2)[/tex]
=[tex](4x+1)(7x^2-x+1).[/tex]
6. [tex]x^2+4x-y^2-2y+3=(x+2)^2-(y+1)^2=(x+y+3)(x-y+1).[/tex]
7. [tex]2x^3-3x^2+3x-1=x^3+(x-1)^3=(2x-1)(x^2-x^2+x+x^2-2x+1)=[/tex]
= [tex](2x-1)(x^2-x+1).[/tex]
8. [tex]x^2+2x-y^2-6y-8=(x+1)^2-(y+3)^2=(x+y+4)(x-y-2).[/tex]
2b⁵-16b² = 2b²(b³-8) = 2b²(b-2)(b²+2b+4)
x²-4xy+4y²+2x-4y = (x-2y)² +2(x-2y) = (x-2y)(x-2y+2)
3a-81a⁴ = 3a(1-27a³) = 3a(1-3a)(1+3a+9a²)
9x²+6xy+y²-6x-2y = (3x+y)² - 2(3x+y) = (3x+y)(3x+y-2)
28x³+3x²+3x+1 = 27х³ + (х+1)³=(3х+х+1)(9х²-3х²-3х+х²+2х+1)=(4х+1)(7х²-х+1)
x²+4x-y²-2x+3 = тут невозможно разложить
2x³-3x²+3x-1 = х³ + (х-1)³ = (х+х-1)(х²-х²+х+х²-2х+1) = (2х-1)(х²-х+1)
x²+2x-y²-6y-8 = (х²+2х+1) - (у²+6у+9) = (х+1)² - (у+3)² = (х-у-2)(х+у+4)