\(\begin{array}{l}a){x^2} - 25 - 4{\rm{x}}y + 4{y^2}\\ = \left( {{x^2} - 4{\rm{x}}y + 4{y^2}} \right) - 25\\ = {\left( {x - 2y} \right)^2} - {5^2}\\ = \left( {x - 2y + 5} \right)\left( {x - 2y - 5} \right)\end{array}\)
\(\begin{array}{l}b){x^3} - {y^3} + {x^2}y - x{y^2}\\ = \left( {{x^3} - {y^3}} \right) + \left( {{x^2}y - x{y^2}} \right)\\ = \left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right) + xy\left( {x - y} \right)\\ = \left( {x - y} \right)\left( {{x^2} + xy + {y^2} + xy} \right)\\ = \left( {x - y} \right)\left( {{x^2} + 2{\rm{x}}y + {y^2}} \right)\\ = \left( {x - y} \right){\left( {x + y} \right)^2}\end{array}\)
\(\begin{array}{l}c){x^4} - {y^4} + {x^3}y - x{y^3}\\ = \left( {{x^4} + {x^3}y} \right) - \left( {{y^4} + x{y^3}} \right)\\ = {x^3}\left( {x + y} \right) - {y^3}\left( {y + x} \right)\\ = \left( {{x^3} - {y^3}} \right)\left( {x + y} \right)\\ = \left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right)\left( {x + y} \right)\end{array}\)
