\(\eqalign{
&a)\; {x^2} + 4x - {y^2} + 4 \cr
& = ({x^2} + 4x + 4) - {y^2} \cr
& = \left( {{x^2} + 2.x.2 + {2^2}} \right) - {y^2} \cr
& = {\left( {x + 2} \right)^2} - {y^2} \cr
& = \left( {x + 2 - y} \right)\left( {x + 2 + y} \right) \cr} \)
\(\eqalign{
& b)\,\,3{x^2} + 6xy + 3{y^2} - 3{z^2} \cr
& = 3.\left( {{x^2} + 2xy + {y^2} - {z^2}} \right) \cr
& = 3.\left[ {\left( {{x^2} + 2xy + {y^2}} \right) - {z^2}} \right] \cr
& = 3.\left[ {{{\left( {x + y} \right)}^2} - {z^2}} \right] \cr
& = 3\left( {x + y - z} \right)\left( {x + y + z} \right) \cr} \)
\(\eqalign{
& c)\,\,{x^2} - 2xy + {y^2} - {z^2} + 2zt - {t^2} \cr
& = \left( {{x^2} - 2xy + {y^2}} \right) + \left( { - {z^2} + 2zt - {t^2}} \right) \cr
& = \left( {{x^2} - 2xy + {y^2}} \right) - \left( {{z^2} - 2zt + {t^2}} \right) \cr
& = {\left( {x - y} \right)^2} - {\left( {z - t} \right)^2} \cr
& = \left[ {\left( {x - y} \right) - \left( {z - t} \right)} \right].\left[ {\left( {x - y} \right) + \left( {z - t} \right)} \right] \cr
& = \left( {x - y - z + t} \right)\left( {x - y + z - t} \right) \cr} \)
