Rút gọn: a) ( x+1) (x+3) - (x-1) (x-3) + 2x (1-x) b) (3x +1) (x+1) - (x+3) (3x - 2) Phân tích đa thức thành nhân tử : a) x^2 + 4y^2 - 4xy - 9 b) x^3 - 1/16x c) x^3 + 4x^2 - 8x - 8 d) x^3 + 6x^2 + 9x - xy^2

\(\begin{array}{l} a){\rm{ }}\left( {{\rm{ }}x + 1} \right)\left( {x + 3} \right) - \left( {x - 1} \right)\left( {x - 3} \right) + {\rm{ }}2x\left( {1 - x} \right)\\ = {x^2} + 3x + x + 3 - \left( {{x^2} - 3x - x + 3} \right) + 2x - 2{x^2}\\ = {x^2} + 4x + 3 - {x^2} + 3x + x - 3 + 2x - 2{x^2}\\ = - 2{x^2} + 10x\\ b){\rm{ }}\left( {3x{\rm{ }} + 1} \right)\left( {x + 1} \right){\rm{ }} - {\rm{ }}\left( {x + 3} \right)\left( {3x - 2} \right)\\ = 3{x^2} + 3x + x + 1 - \left( {3{x^2} - 2x + 9x - 6} \right)\\ = 3{x^2} + 4x + 1 - 3{x^2} + 2x - 9x + 6\\ = - 3x + 7 \end{array}\)