$\begin{array}{l} a){x^2} - 6xy + 9{y^2}\\ = {\left( {x - 3y} \right)^2}\\ b)4{x^2} - 12xy + 9{y^2}\\ = {\left( {2x} \right)^2} - 2.\left( {2x} \right).3y + {\left( {3y} \right)^2}\\ = {\left( {2x - 3y} \right)^2}\\ c)\left( {5 + 2x} \right)\left( {2x - 5} \right)\\ = \left( {2x + 5} \right)\left( {2x - 5} \right)\\ = 4{x^2} - 25\\ d){\left( {x + 2y} \right)^2} + 2\left( {x + 2y} \right) + 1\\ = {\left( {x + 2y + 1} \right)^2}\\ e)16{x^2} - 9{y^2}\\ = {\left( {4x} \right)^2} - {\left( {3y} \right)^2}\\ = \left( {4x - 3y} \right)\left( {4x + 3y} \right)\\ f){\left( {2x + 3y} \right)^2} + 2\left( {2x + 3y} \right) + 1\\ = {\left( {2x + 3y + 1} \right)^2} \end{array}$
