\(a_1,=\left(x^3+x^2-2x^2-2x+3x+3\right):\left(x+1\right)\\ =\left(x+1\right)\left(x^2-2x+3\right):\left(x+1\right)\\ =x^2-2x+3\\ a_2,=\left(2x^2+3y^2\right)^2:\left(2x^2+3y^2\right)=2x^2+3y^2\\ b_1,=\left(x^3-7x^2+x^2-7x-2x+14\right):\left(x-7\right)\\ =\left(x-7\right)\left(x^2+x-2\right):\left(x-7\right)\\ =x^2+x-2\\ b_2,=\left(8ab-7m^2n\right)\left(8ab+7m^2n\right):\left(8ab+7m^2n\right)=8ab-7m^2n\\ c,=\left(3x-2y^2\right)\left(9x^2+6xy^2+4y^4\right):\left(3x-2y^2\right)\\ =9x^2+6xy^2+4y^4\\ d,=\left(3x+2y^2\right)\left(9x^2-6xy^2+4y^4\right):\left(9x^2-6xy^2+4y^4\right)\\ =3x+2y^2\)