Question

разложите на множители 1)5m²n-6an+10m²-3an²= 2)8mn³-24n²-7mn+21= 3)ax²+yx²+ax+cx²+yx+cx= 4)12a²y²-6ayc+3ac²-6a²yc-c+2ay= ребята помогите пожалуйста

Answer 1

5m²n-6an+10m²-3an²=(5m²n+10m²)+(-6an-3an²)=5m²(n+2)-3an(2+n)=(n+2)(5m²-3an)

8mn³-24n²-7mn+21=(8mn³-7mn)+(-24n²+21)=mn(8n²-7)-3(8n²-7)=(8n²-7)(mn-3)

ax²+yx²+ax+cx²+yx+cx=(ax²+ax)+(yx²+yx)+(cx²+cx)=ax(x+1)+yx(x+1)+cx(x+1)=
=(x+1)(ax+yx+cx)

12a²y²-6ayc+3ac²-6a²yc-c+2ay=(12a²y²-6ayc)+(3ac²-6a²yc)+(-c+2ay)=
=6ay(2ay-c)-3ac(-c+2ay)+(-c+2ay)=6ay(2ay-c)-3ac(2ay-c)+(2ay-c)=
=(2ay-c)(6ay-3ac+1)