Question

помогите разложить на множники​

Answer 1

$\displaystyle\bf\\1)\\\\b^{2} +ab-2a^{2}-b+a=\Big(b^{2} -a^{2} \Big)+\Big(ab-a^{2} \Big)-\Big(b-a\Big)=\\\\=\Big(b-a\Big)\Big(b+a\Big)+a\Big(b-a\Big)-\Big(b-a\Big)=\Big(b-a\Big)\Big(b+a+a-1\Big)=\\\\=\Big(b-a\Big)\Big(b+2a-1\Big)\\\\\\2)\\\\x^{3} - y^{3} +3y^{2} -3y+1=x^{3} -\Big(y^{3}-3y^{2} +3y-1\Big) =x^{3}-\Big(y-1\Big)^{3} =\\\\=\Big(x-y+1\Big)\cdot\Big[x^{2} -x\Big(y-1\Big)+\Big(y-1\Big)^{2} \Big]=\\\\=\Big(x-y+1\Big)\Big(x^{2} -xy+x+y^{2} -2y+1\Big)$

$\displaystyle\bf\\3)\\\\8x^{3} +y^{3} +6y^{2} +12y+8=8x^{3}+\Big(y^{3} +6y^{2} +12y+8\Big)=\\\\=\Big(2x\Big)^{3} +\Big(y+2\Big)^{3} =\Big(2x+y+2\Big)\Big(4x^{2} +y^{2} -2xy-4x+4y+4\Big)$