`a)`

`VT = a(b+c) - b(a-c)`

`VT = ab + ac - ba + bc`

`VT = (ab - ab) + ac + bc`

`VT = ac + bc`

`VT = c(a+b) = VP`

`=> a(b+c) - b(a-c) = c(a+b)`

`b)`

`VT = (a-b) + (c-d)`

`VT = a - b + c - d`

`VT = (a+c) - (b+d) = VP`

`=> (a-b) + (c-d) = (a+c) - (b+d)`

`c)`

`VT = a(b-c) - a(b+d)`

`VT = ab - ac - ab - ad`

`VT = (ab - ab) - ac - ad`

`VT = -ac - ad`

`VT = -a(c+d) = VP`

`=> a(b-c) - a(b+d) = -a(c+d)`

`d)`

`VT = (a-b) - (c-d)`

`VT = a - b - c + d`

`VT = (a+d) - b - c`

`VT = (a+d) - (b+c) = VP`

`=> (a-b) - (c-d) = (a+d) - (b+c)`

`e)`

`VT = (a-b) - (c-d) + (b+c)`

`VT = a - b - c + d + b + c`

`VT = a + (-b+b) + (-c+c) + d`

`VT = a + d = VP`

`=> (a-b) - (c-d) + (b+c) = a+d`

`f)`

`VT = (a-b) + (c-d) - (a+c)`

`VT = a - b + c - d - a - c`

`VT = (a-a) + (c-c) - b - d`

`VT = -b - d`

`VT = -(b+d) = VP`

`=> (a-b) + (c-d) - (a+c) = -(b+d)`