$\begin{array}{l} a){a^2}{x^2} - {a^2}{y^2} - {b^2}{x^2} + {b^2}{y^2}\\ = {a^2}\left( {{x^2} - {y^2}} \right) - {b^2}\left( {{x^2} - {y^2}} \right)\\ = \left( {{x^2} - {y^2}} \right)\left( {{a^2} - {b^2}} \right)\\ = \left( {x - y} \right)\left( {x + y} \right)\left( {a - b} \right)\left( {a + b} \right)\\ b)B = (x + 2)(x + 3)(x + 4)(x + 5) - 24\\ = \left( {{x^2} + 5{\rm{x}} + 2{\rm{x}} + 10} \right)\left( {{x^2} + 4{\rm{x}} + 3{\rm{x}} + 12} \right) - 24\\ = \left( {{x^2} + 7{\rm{x}} + 10} \right)\left( {{x^2} + 7{\rm{x + 12}}} \right) - 24\\ dat:{x^2} + 7{\rm{x + 11 = t}}\\ B = \left( {t - 1} \right)\left( {t + 1} \right) - 24\\ = {t^2} - 1 - 24\\ = {t^2} - 25\\ = \left( {t - 5} \right)\left( {t + 5} \right)\\ = \left( {{x^2} + 7{\rm{x}} + 11 - 5} \right)\left( {{x^2} + 7{\rm{x}} + 11 + 5} \right)\\ = \left( {{x^2} + x + 6{\rm{x}} + 6} \right)\left( {{x^2} + 7{\rm{x}} + 16} \right)\\ = \left[ {x\left( {x + 1} \right) + 6\left( {x + 1} \right)} \right]\left( {{x^2} + 7{\rm{x}} + 16} \right)\\ = \left( {x + 1} \right)\left( {x + 6} \right)\left( {{x^2} + 7{\rm{x}} + 16} \right)\\ c{X^2} - 2014x - 2013\\ = {x^2} - 2014{\rm{x}} + 1014049 - 1016062\\ = {\left( {x - 1007} \right)^2} - 1016062\\ = \left( {x - 1007 - \sqrt {1016062} } \right)\left( {x - 1007 + \sqrt {1016062} } \right)\\ d){x^2} - 2xy + {y^2} + 3x - 3y - 10\\ = {\left( {x - y} \right)^2} + 3\left( {x - y} \right) - 10\\ = {\left( {x - y} \right)^2} - 2\left( {x - y} \right) + 5\left( {x - y} \right) - 10\\ = \left( {x - y} \right)\left( {x - y - 2} \right) + 5\left( {x - y - 2} \right)\\ = \left( {x - y - 2} \right)\left( {x - y + 5} \right) \end{array}$