Phương pháp giải:

Lời giải chi tiết:

Hướng dẫn giải chi tiết:

\(a)\;{x^2} + 4x - {y^2} + 4 = \left( {{x^2} + 4x + 4} \right) - {y^2} = \left( {{x^2} + 2.2.x + {2^2}} \right) - {y^2} = {\left( {x + 2} \right)^2} - {y^2} = \left( {x - y + 2} \right)\left( {x + y + 2} \right)\)

\(\begin{array}{l}b)\;4{x^2} - 25 - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\= {\left( {2x} \right)^2} - {5^2} - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\= \left( {2x - 5} \right)\left( {2x + 5} \right) - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\= \left( {2x - 5} \right)\left( {2x + 5} \right) + \left( {2x + 7} \right)\left( {2x - 5} \right)\\= \left( {2x - 5} \right)\left( {2x + 5 + 2x + 7} \right) = \left( {2x - 5} \right)\left( {4x + 12} \right)\end{array}\)

\(c)\;{\left( {2{x^2} - y} \right)^2} - 64{y^2} = {\left( {2{x^2} - y} \right)^2} - {\left( {8y} \right)^2} = \left( {2{x^2} - y - 8y} \right)\left( {2{x^2} - y + 8y} \right) = \left( {2{x^2} - 9y} \right)\left( {2{x^2} + 7y} \right)\)

\(d)\; - {x^3} + 6{x^2}y - 12x{y^2} + 8{y^3} = {\left( { - x} \right)^3} + 3.{x^2}.2y + 3.\left( { - x} \right).{\left( {2y} \right)^2} + {\left( {2y} \right)^3} = {\left( { - x + 2y} \right)^3} = {\left( {2y - x} \right)^3}\)

\(\begin{array}{l}e)\;{x^8} - {y^8} = {\left( {{x^4}} \right)^2} - {\left( {{y^4}} \right)^2} = \left( {{x^4} + {y^4}} \right)\left( {{x^4} - {y^4}} \right)\\ = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {{x^2} - {y^2}} \right) = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\left( {x - y} \right)\end{array}\)