Question

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ПОМОГИТЕ ПОЖАЛУСТА


1) x(3) – b(2) – ax – ab =
2) 3b + bc + 3ac + 9a =
3) a(2)x(2) – x(6) =
4) a(2)x(2) – y(4) =
5) c(2) – 4c + 4 – 4x(2) =
6) c(2) – 6c + 9 – 4x(2) =
7) 4c(2) – 20c + 25 – 9a(2) =
8) y(2)x + y + yx(2) + 4xy + 4 =
9) 3x(2) + 2x – xy – 2y(2) + y(3) – 3xy(2) =
10) x(2) + x – xy – y(2) + y(3) – xy(3) =
11) a(2)x + a + ax(2) + x +2ax + 2 =

Answer 1

1.  x²-b²-ax-ab=(x-b)x+b)-a(x+b)=(x+b)(x-b-a).
2. 3b+bc+3ac+9a=b(3+c)+3a(3+c)=(3+c)(b+3a).
3. a²x²-x⁶=x²(a²-x⁴)=x²(a-x²)(a+x²).
4. a²x²-y⁴=(ax-y²)(ax+y²).
5. c²-4c+4-4x²=(c²-4c+4)-(2x)²=(c-2)²-(2x)²=(c-2-2x)(c-2+2x)
6. c²-6c+9-4x²=(c²-6c+9) -(2x)²=(c-3)²-(2x)²=(c-3-2x)(c-3+2x).
7. 4c²-20c+25-9a²=(4c²-2·2·5·c+25)-(3a)²=(2c-5)²-(3a)²=
    =(2c-5-3a)(2c-5+3a).
8. 
9. 3x²+2x-xy-2y²+y³-3xy²=(3x²-3xy²)+(2x-2y²)-(xy-y³)=
    =3x(x-y²)+2(x-y²)-y(x-y²)=(x-y²)(3x+2-y).
10. x²+x-xy-y²+y³-xy³=(x²-xy³)+(x-y²)-(xy-y³)=
      =xy(x-y²)+1·(x-y²)-y(x-y²)= (x-y²)(xy+1-y).
11. a²x+a+ax²+x+2ax+2=(a²x+a)+(ax²+x)+(2ax+2)=
      =a(ax+1)+x(ax+1)+2(ax+1)= (ax+1)(a+x+2).