Long example
A�B�C�D� + A�BC�D� + A�BD + A�BC�D + ABCD + ACD� + B�CD�
= A�C�D�(B� + B) + A�BD(1 + C�) + ABCD + ACD� + B�CD�
= A�C�D� + A�BD + ABCD + ACD� + B�CD�
= A�C�D� + BD(A� + AC) + ACD� + B�CD�
= A�C�D� + BD(A� + C) + ACD� + B�CD� (Since X + X�Y = X + Y)
= A�C�D� + A�BD + (BCD + ACD�) + B�CD�
= A�C�D� + A�BD + (BCD + ACD� + ABC) + B�CD�
= A�C�D� + (A�BD + ABC + BCD) + (ABC + B�CD� + ACD�)
= AC�D� + A�BD + ABC + B�CD�