`1,`

`5x^2 -10x + 5 -45t^2`

`= 5 (x^2 -2x + 1 - 9x^2 )`

`= 5 [ ( x^2 -2x + 1 )-9x^2 ]`

`=5 [ ( x-1 )^2- ( 3x )^2 ]`

`= 5 ( x-1 -3x )( x-1 + 3x )`

`=5 ( -2x -1 )(4x -1 )`

`2,`

` x^2 - 36y^2t^2 -10x + 25`

`= ( x^2 -10x + 25 ) - 36y^2t^2`

`= ( x-5 )^2 - ( 6yt )^2`

`= ( x-5-6yt )( x + 5 + 6yt)`

`3,`

` x^2 -2xy + y^2 -16z^2`

`= ( x^2-2xy + y^2 ) - ( 4z )^2`

`= ( x-y )^2 - (4z )^2`

`= ( x-y -4z )( x-y + 4z )`

`4,`

`8x^2 -16x + 8 -32y^2`

`= 8 ( x^2 -2x + 1 -4y^2 )`

`= 8 [ ( x-2x + 1 ) - 4y^2 ]`

`= 8 [ ( x-1 )^2 -(2 y )^2 ]`

`=8 ( x-1-2y )( x-1 + 2y )`