How do i factor this out?
why does the x-y disappear and the other stays behind? can anyone explain this to me?

because in first expressions they common out x and y and then it get cancel out

Step-by-step explanation:

See answer in above picture

AC bisects ∠BAD, => ∠BAC=∠CAD (1)

thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given),

                                      ∠BAC=∠CAD      [from (1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence,      by AAS axiom, ΔABC ≅ ΔADC,

Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

Hence, BC=DC proved.