Why XY + XZ + YZ can be simplified into XY + Z(X¬Y + ¬XY) in boolean algebra?

Question

I not understand why the first boolean expression on the question can be simplified into the last. Please help me.

Answer 1

XY + Z(X ⊕ Y)
= XY + Z(X¬Y + ¬XY)                           // Expand XOR operation
= XY + X¬YZ + ¬XYZ                            // Distribute AND over OR
= XYZ + XY¬Z + X¬YZ + ¬XYZ                    // Expand XY
= (XYZ + XY¬Z) + (XYZ + X¬YZ) + (XYZ + ¬XYZ)  // Copy XYZ and add parens
= XY + XZ + YZ                                // Remove trivial X+¬X = 1's

Reassembly is the reverse of disassembly.