[tex]a) \frac{ {x}^{2} }{9} - {y}^{2} = \frac{ {x}^{2} }{ {3}^{2} } - {y}^{2} = {( \frac{x}{3}) }^{2} - {y}^{2} = ( \frac{x}{3} - y)( \frac{x}{3} + y)[/tex]
[tex]b) \frac{4 {a}^{2} }{9} - {b}^{2} = \frac{ {2}^{2} \times {a}^{2} }{ {3}^{2} } - {b}^{2} = \frac{ {(2a)}^{2} }{ {3}^{2} } - {b}^{2} = {( \frac{2a}{3} )}^{2} - {b}^{2} = ( \frac{2a}{3} - b)( \frac{2a}{3} + b)[/tex]
[tex]e) \frac{ {a}^{2} }{121} - \frac{16 {b}^{2} }{25} = \frac{ {a}^{2} }{ {11}^{2} } - \frac{ {4}^{2} \times {b}^{2} }{ {5}^{2} } = {( \frac{a}{11}) }^{2} - \frac{ {(4b)}^{2} }{ {5}^{2} } = {( \frac{a}{11} )}^{2} - {( \frac{4b}{5}) }^{2} = ( \frac{a}{11} - \frac{4b}{5} )( \frac{a}{11} + \frac{4b}{5} )[/tex]
[tex]f) \frac{36}{49} {a}^{2} {b}^{2} {c}^{2} - 25 = \frac{ {6}^{2} }{ {7}^{2} } {(abc)}^{2} - {5}^{2} = \frac{ {(6abc)}^{2} }{ {7}^{2} } - {5}^{2} = {( \frac{6abc}{7} )}^{2} - {5}^{2} = ( \frac{6abc}{7} - 5)( \frac{6abc}{7} + 5)[/tex]
[tex]i) \frac{ {x}^{2} }{9 {y}^{2} } - \frac{25 {z}^{2} }{4 {t}^{2} } = \frac{ {x}^{2} }{ {3}^{2} \times {y}^{2} } - \frac{ {5}^{2} \times {z}^{2} }{ {2}^{2} \times {t}^{2} } = \frac{ {x}^{2} }{ {(3y)}^{2} } - \frac{ {(5z)}^{2} }{ {(2t)}^{2} } = {( \frac{x}{3y} )}^{2} - {( \frac{5z}{2t} )}^{2} = ( \frac{x}{3y} - \frac{5z}{2t} )( \frac{x}{3y} + \frac{5z}{2t} )[/tex]
