Question

Разложить на множители 1)m^3-m-am^2+a 2)ay-2ab+2by-y^2 3) x^2+4yz-xy-4xz 4)ay^2+2a^2-a^3-2y^2 5)a^2+ab+az+bx 6)6m-12-2n+mn 7)x+y-x^2-xy 8)4ab^2+4ab+a+ab 9)5m^2n-6an+10m^2-3an^2 10)8mn^3-24n^2-7mn+21 11)ax^2+yx^2+ax+cx^2+yx+cx 12) 12a^2y^2-6ayc+3ac^2-6a^2yc-c+2ay

Answer 1

1) $m^{3}-m-am^{2}+ a = m(m^{2} -1)-a(m^{2}-1)= (m^{2}-1)(m-a)$

2) $ay-2ab+2by-y^{2} = a(y-2b)-y(y-2b) = (y-2b)(a-y)$

3) $x^{2}+4yz-xy-4xz= x(x-y) -4z (x-y) = (x-y)(x-4z)$

4) $ay^{2}+2a^{2}-a^{3}-2y^{2} = y^{2}(a-2) - a^{2} (a-2) = (a-2)(y^{2}-a^{2}) \\ = (a-2)(y-a)(y+a)$

5) никак, может быть ошибка в написании

6) 6$6m-12-2n+mn = 6(m-2) -n(m-2) = (m-2)(6-n)$

7) $x+y-x^{2}-xy = x+y - x(x+y) = (x+y)(1-x)$

8) $4ab^{2} +4ab+a+ab = a(4b(b+1)+ 1+b)) = a(b+1)(4b+1)$

9) $5m^{2}n-6an+10m^{2}-3an^{2} = 5m^{2}(n+2)-3an(2+n) =\\ = (n+2)(5m^{2}-3an)$

10) $8mn^{3}-24n^{2}-7mn+21 = 8n^{2} (mn-3) -7(mn-3) =\\ = (mn-3)(8n^{2}-7)$

11) $ax^{2} +yx^{2}+ax+cx^{2}+yx+cx = x^{2}(a+y+c) + x(a+y+c) = \\ = x(x+1)(a+y+c)$

12) $12a^{2}y^{2}-6ayc+3ac^{2}-6a^{2}yc-c+2ay = \\ =6a^{2}y(2y-c) - 3ac(2y-c) +2ay-c = \\=(2yc-c)3a(2ay-c) +2ay-c= (2ay-c)(3a(2yc-c)+1)$